We have a small 1/2 bathroom on the main floor of our house. We just started getting a sewage odor from the sink the last couple days. I pulled the drain stop out and pulled out hair, etc. I think I cleaned most of the stuff out. We just got a new washer and dryer and installed it downstairs about 1 week ago. Could this be related? How do we fix it if so?

Most bad smells in tubs, lavatorys and showers are caused by rotting hair matted with grease from the soap. Try this for the smell. Tonight before bedtine Take a 1/2 gallon of bleach and pour it down the drain and let set over night. Next morning ,(and this is important) flush out the drain with two large pans of boiling water to loosen the grease and flush the mess out. The bleach will make the hair slippery and began to dissolve it and the hot water will melt the grease and flush the mess away.
This should make your drains smell better. Good luck, Tom