Currently have washer and dryer in the basement. Would like to hook up washer and dryer immediately above these in my garage. The current drain system to the washer and dryer does not have a vent, do I need to add one. If I run the drain for the washer in the garage can it be connected to the current drain pipe, and if so how?

Connect it as shown in the enclosed drawing. You can run vent all the way through the roof - or connected it with another existing vent about 48" above the floor on the 1st floor...