How long can I wear wool socks before I have to wash them?

This really depends on what you wear the socks with, and how you care for them when you aren't wearing them.

Socks need to be washed regularly to prevent bacteria growth, but wool helps keep them smelling nice because of the properties of wool. If the socks are treated wool, they won't have many of the same benefits as untreated wool.

Even though they smell fine, they should be washed after a week, especially if you are wearing boots or sneakers that completely cover the foot. If you are wearing these with sandals or another open style of shoe, you could probably go 2 weeks without washing because of the ventilation the shoe gives.

I would just wash them in the sink with a bit of fabric soap, then hang them to dry in the bathroom overnight so they are ready to wear in the morning.

When they walk away.

I don't wash my "thick woolies" every time I wear them. But I do wear thin liner socks under them and change to fresh liner socks at least once daily. I recommend that you do likewise. That you don't notice any smell is a very different thing from there not being any smell.

as long as you can handle the smell from them

until they are stinky

They should be washed after each day's wear. Your feet probably sweat and eventually fungus will grow and you'll get tinea.

stop that

change everyday

I doubt that. YOU just can't smell them anymore.