I'm currently working in and picking up my checks in Texas. I have a dorm room I'm living in over the summer in Texas. I also have an apartment in Oklahoma where I live year round and on the weekends which is where I deposit my checks. Currently they are not withholding state taxes from my check.

Do I need to pay Oklahoma state taxes or do I not have to pay since Texas doesn't have any?

Also can I deduct car expenses like gas and maintenance since I'm commuting as well?

You will report this income on your Oklahoma tax return. You can deduct your expenses as itemized deduction -- employee business expenses.
Read about working/living in two states: Your U.S. Tax Return: Working or Living in Two or More states
About employee business expenses: Your U.S. Tax Return: Itemized Deductions

Your commuting expenses are NOT deductible.

Like MukatA said, you are liable for Oklahoma state income taxes as an Oklahoma resident and will be until you change your residence to Texas.