I have to go to the post office for my job. Can I claim the gas I use on that trip?

If you are an employee, no, you cannot claim any expenses related to work as a W-2 employee.

 

If you are a sole proprietor, then yes, you can claim the gas or mileage you use to go to the post office. 

 

Deducting Auto Expenses

 

IRS Mileage rates