I'm a resident at a college that's in a different state from my home. I'm applying for a job near campus. On the section where it asks my address, should I give my home address or my college address?

Use your college address, since that's where you're staying & near work. Some applications have room for 2 addresses - eg. home & mail, etc. Mark one "Permanent Address" & give your home/parents' address. But you're at school & looking for basically a student's job.

You are applying for a job near where you are studying so you put that address or they will think you are applying form another state and will be traveling

Where do you want your w-2s sent?

Because they'll know you're a student and that you live locally. What matters is where they'll eventually send your last paycheck and your w2.s

I would give your home address.