So I was invisible using greater invisibility, I cast Magic Jar and possess a creature, at the time I was flying with overland flight, so what happens to my body stay invisible and stay in the air or float to the ground(ring of feather fall)?
Whether or not spell effects stay with your body or travel into the new host is something I've been trying to determine for YEARS without success. The best solution I've come up with is to let the caster decide what effects follow and which don't, since (1) both your body and your possessing spirit are "you" and (2) a spellcaster should naturally have such control over his own magic.
Throw in the concept of curses and ability damage to the equation along with spell effects and you've just opened up a whole can of worms.
Well assuming that all abilities were left on my real body, would I remain flying after my body falls unconscious?
I'd stick with what RD said; as the caster, you choose whether overland flight stays with your physical body, or moves to the new creature you possessed.
If you're possessing a flying creature, then I'd say the most risk your body would have would be spell duration, and the wind currents carrying it wherever the GM deemed.