Han in general being an overly comedic singer, with a tendency to ask for ridiculous items in absurdly specific numbers such as 17 frogs.
A New Hope
C-3PO having an Indian accent.
Luke and Owen having deep southern country accents.
And R2-D2 acting and sounding like a little girl.
The fact that the many characters without visible mouths makes it really easy to just dub in whatever they want. Especially stormtroopers and aliens.
Luke's introduction:
Luke: A big grey thing chased me up the mountain and froze!
Owen: Remember what I said about that? That was your shadow!
Luke: Oh yeah, that thing.
Leia's hologram, and Luke's reaction:
Leia: I want a wooden snowman, but no one sells them. *knocking at door* I'll be right out! *crouches to insert plans, farts* (repeat on loop)
Luke: I want her to dance!
R2-D2: She does not dance.
C-3PO: Come on, make her dance for him!
R2-D2: That's not how it works.
*message plays*
Luke: Holy chicken, she's beautiful. *points* I wish you were real!
Obi-Wan's reason for seeking Han's help:
Ben: Look, I just need the pickaxe of Cortez and the mystical diamonds!
This exchange:
Han: Well, why don't you just move to Nevada, dude?
Luke: Because I heard it was a bad part of Mexico! Did you hear him? He doesn't even know geography!note Nevada actually WAS a part of Mexico for a time
Negotiations with Greedo:
Greedo: Listen, I've been sent here to collect all your fireworks, okay?
Han: Aw, just let me set 'em off at the meeting.
Greedo: Well, maybe I will if you give me your grilled meat.
Han: I don't have any grilled meat.
Greedo: Okay...um, do you have any pets?
Han: I have a monkey in a bottle...
Greedo: Does your monkey go "hoo hoo HOO"?
Han: No, that's the pet giraffe. *immediate cut to Greedo being shot*
Musings aboard the Falcon:
Han: Y'know, I should build a baby Taco Bell. The sign would be kinda cute.
Han singing:
Han: ♪I love it when you say that/A lot of great skaters bust their teeth♪
Obi-Wan: That song didn't make a bit of sense, and I don't like it!
Han: ♪There's an extra part that's worth it/And I'll sing it if I get/To clip your nails♪ Okay, anyway, I'm hopping on the can.
Food?
Han: Ugh, I'm going crazy, I'm so hungry.
Luke: Well, I could make grilled cheese...
Han: No offense, kid, I don't think you even know how to boil water.
Luke meets Leia:
Luke: I was a dog walker, you're really cute!
Leia: Ew.
Luke: Oh, you're really cute, and I forgot to wash earlier, but my bed is open!
Leia: No, person!
Luke: That's okay!
The lightsabers sounding like two plastic props smacking together, much like they would have on-set.