Thanks to the Supergirl Wiki and 4chan for digging these up.
Update: Even more videos can be found here.
Kara:
Super Girl Audition from Kristina Miller on Vimeo.
Kaleina Cordova - Supergirl Audition from Kaleina Cordova on Vimeo.
Alex:
SuperGirl - self tape 1. ALEX from Rachael Elizabeth on Vimeo.
BRITTANY BURCH - SUPER GIRL Audition from sherman edwards on Vimeo.
James:
Self Tape Audition - Supergirl from Scot Cooper on Vimeo.
Audition Supergirl from Fernando Belo on Vimeo.
Wynn:
Miguel Pinzon audition for SUPERGIRL role of WYNN from 23 Management Group on Vimeo.
Dialogue from the scenes are as follows:
JAMES: Excuse me.
KARA: Derek, from editorial. Sorry, haven't done your research yet... Wow, no. Not Derek. His bones are way less dense... Not that I know that, because that would be like... Having a dual energy X-Ray observatory meter inside your eyes, which would be crazy...
JAMES: Yeah, it's... It's James.
KARA: Right, the new unit photographer from Metropolis, I know that because you're on a post-it... Oh, no. I was supposed to get those proofs from you...
JAMES: 10 minutes ago, yeah, I figured I'd bring them up so you wouldn't get in trouble with your boss.
KARA: Thanks, that's... That's him.
JAMES: Superman, yes. How did you know?
KARA: Of course it's him. Because you're famous for taking pictures of him.
JAMES: Oh, God, am I really that derivative? Time for a new subject.
KARA: Is it true you're friends?
JAMES: Yeah... Yeah, I guess. I wouldn't have pegged you for a Super-fan.
KARA: He feels more like... family... to me.
JAMES: That's what they all say. Go on, I know that look. Ask me all the questions, I've heard them all. How tall is he? What does he eat for breakfast? Does he sleep?
KARA: Were you scared of him? When you first saw what he could do, were you scared of him?
JAMES: ... Haven't heard that one. Was I scared? I was just starting out. Mr. White sent me to cover a house fire. People... Kids... trapped inside. At some point, the firefighters... All they could do was pray. And then, there he was. A person, in the sky, flying. He cut down this giant tree with a ray of heat from his eyes and made a bridge so a family could escape, and when the tree caught on fire, he cooled it off with a blast of freezing air from his mouth. I should've been terrified, but I wasn't. Something about him made me feel...
KARA: Safe?
JAMES: Yeah, that's right. That's why he's him, I guess. So, huh... Do you have superpowers?
KARA: What? That's an absurd accusation, I'm just a regular human person who has a lot to do before she can leave tonight.
JAMES: No, I just mean because your boss is coming, and she really pissed. Later, Kara.
Source:
ALEX: Why can't you just text me whatever your big thing is? I've got a meeting with Henshaw in five...
KARA: Can't see your face over the phone.
ALEX: OK, you have three seconds.
KARA: I did it, Alex. I did what you always wanted me to do.
ALEX: Your hair looks exactly the same.
KARA: No, I saved them. I did it, I stopped them from going over the bridge, those people are alive because of something I did.
ALEX: You could've been killed.
KARA: How? I could bend this steel desk into a little ball if I wanted to, you've seen what I can do.
ALEX: Then they could've been killed, it's not like you've had a lot of practice stopping trains.
KARA: You always said that if you had my powers, you'd use them to change the world. I came here to say you were right, I'm going to.
ALEX: How?
KARA: By finally being the person I was sent here to be.
ALEX: You have not thought this through. You expose your powers. Outside, in daylight, to the general public. Do you have any idea what the odds are someone has taken a photo, maybe a video, of you stopping that train with your hands? I'm going with 100%. You're probably already trending.
KARA: They would've died without me. I don't get it, I thought you'd be proud.
ALEX: Our whole childhood, you hid your abilities like they were disabilities. You made me, our family, your co-conspirators. And now you walk in here, announcing a career change? What's next, law school?
KARA: Today felt like the first day of my life. I felt like I was back home.
ALEX: In Midvale?
KARA: Krypton. I mean...I had to do something spectacular just to feel normal.
ALEX: Whatever you're going through, it'll pass. Just don't do something you're gonna regret.
KARA: I just told you about the best moment of my life, and you can't even be happy for me.
ALEX: Kara... You may have his abilities, but you're not him.
KARA: No. You're right, I'm not. I am Kara Zor-El. Daughter of Alura. And I'm gonna start living like it.
KARA: Can't see your face over the phone.
ALEX: OK, you have three seconds.
KARA: I did it, Alex. I did what you always wanted me to do.
ALEX: Your hair looks exactly the same.
KARA: No, I saved them. I did it, I stopped them from going over the bridge, those people are alive because of something I did.
ALEX: You could've been killed.
KARA: How? I could bend this steel desk into a little ball if I wanted to, you've seen what I can do.
ALEX: Then they could've been killed, it's not like you've had a lot of practice stopping trains.
KARA: You always said that if you had my powers, you'd use them to change the world. I came here to say you were right, I'm going to.
ALEX: How?
KARA: By finally being the person I was sent here to be.
ALEX: You have not thought this through. You expose your powers. Outside, in daylight, to the general public. Do you have any idea what the odds are someone has taken a photo, maybe a video, of you stopping that train with your hands? I'm going with 100%. You're probably already trending.
KARA: They would've died without me. I don't get it, I thought you'd be proud.
ALEX: Our whole childhood, you hid your abilities like they were disabilities. You made me, our family, your co-conspirators. And now you walk in here, announcing a career change? What's next, law school?
KARA: Today felt like the first day of my life. I felt like I was back home.
ALEX: In Midvale?
KARA: Krypton. I mean...I had to do something spectacular just to feel normal.
ALEX: Whatever you're going through, it'll pass. Just don't do something you're gonna regret.
KARA: I just told you about the best moment of my life, and you can't even be happy for me.
ALEX: Kara... You may have his abilities, but you're not him.
KARA: No. You're right, I'm not. I am Kara Zor-El. Daughter of Alura. And I'm gonna start living like it.
Source:
WYNN: This is straight from editorial. Have you seen her? I mean, she looks like every girl that never talked to me in high school and college.... I mean, she's the female version of him!
KARA: No, she's not the female him. She's her own thing, completely unique, unaffiliated, individual...
WYNN: Imagine the possibilities. The Man of Steel... In girl form. I mean, her powers could possibly rival his.
KARA: Not "possibly" rival his, she's an equal.
WYNN: She didn't bother fabricating a costume.
KARA: She didn't had time, she had to act fast.
WYNN: First impressions count, though, she's very dirty.
KARA: She's lifting a train.
WYNN: Barefoot, needs a pedicure.
KARA: She's saving peoples' lives!
WYNN: She's very cool. Superpowers plus boobs, I mean, she's gonna make it very difficult for women to think they can date him as long as someone like her is out there.
KARA: Stop saying stuff like that. Who cares what she looks like? She's a hero.
WYNN: You know, Kara, you're right. My superficiality is everything that's wrong with this city. Where were you born?
KARA: Up north?
WYNN: Rhetorical. What I'm saying is that people living in National City weren't actually born in National City. We moved here to make it, but we got caught up with the way we look and the clothes and the cars and the laser hair removal that we forget to see each other. I mean, this morning when I was in line waiting for my cream cheese I noticed people were actually talking to each other.
KARA: What did they say?
WYNN: Who cares, we were on our phones. Connecting over an alien. She's already helping us more than she knows.
KARA: I think you're starting to get it.
WYNN: This big city is already feeling a lot smaller now thanks to the new Super-Chick,
KARA: We're gonna have to work on the name.
WYNN: Yeah.
KARA: No, she's not the female him. She's her own thing, completely unique, unaffiliated, individual...
WYNN: Imagine the possibilities. The Man of Steel... In girl form. I mean, her powers could possibly rival his.
KARA: Not "possibly" rival his, she's an equal.
WYNN: She didn't bother fabricating a costume.
KARA: She didn't had time, she had to act fast.
WYNN: First impressions count, though, she's very dirty.
KARA: She's lifting a train.
WYNN: Barefoot, needs a pedicure.
KARA: She's saving peoples' lives!
WYNN: She's very cool. Superpowers plus boobs, I mean, she's gonna make it very difficult for women to think they can date him as long as someone like her is out there.
KARA: Stop saying stuff like that. Who cares what she looks like? She's a hero.
WYNN: You know, Kara, you're right. My superficiality is everything that's wrong with this city. Where were you born?
KARA: Up north?
WYNN: Rhetorical. What I'm saying is that people living in National City weren't actually born in National City. We moved here to make it, but we got caught up with the way we look and the clothes and the cars and the laser hair removal that we forget to see each other. I mean, this morning when I was in line waiting for my cream cheese I noticed people were actually talking to each other.
KARA: What did they say?
WYNN: Who cares, we were on our phones. Connecting over an alien. She's already helping us more than she knows.
KARA: I think you're starting to get it.
WYNN: This big city is already feeling a lot smaller now thanks to the new Super-Chick,
KARA: We're gonna have to work on the name.
WYNN: Yeah.
Source: