I'm 36 weeks and have an oblique lying baby. Will he move or will this affect my birth?

Oblique Lie at 36 wk. An oblique lie (assuming this is head-down oblique) will convert to a longitudinal lie (head-down, cephalic, or "normal") 99% of the time by the time of labor. About 1% of the time, the baby may convert to a transverse lie. Obviously a transverse lie is not compatible with vaginal delivery, which would affect the birth.
Could settle or not. Baby either will or won't get into proper position. Sometimes an OB can try a version (external turning maneuver) to move baby into better position when you are closer to delivery.If baby doesn't settle, you'll need to expect a surgical delivery.