When I flush the toilet there is a lot of noise (glug, glug glug) in the tub drain. What causes that?

Probably a blocked vent. Tub is being used as a vent, the glug is the air venting through the tub trap.

I agree and depending on you weather it may be difficult to get on your roof.

I agree with both experts. You have a blocked lavatory vent. They can only be snaked from the roof. Put out enough snake to reach the base and 15 put more. As Bob pointed out, you may have to wait for better weather to do thi job. Good luck, stay warm, and happy new year. Tom