Toyota mr2 gearbox oil and engine oil sump

Well you're on the wrong side of the engine bay there. 
Engine oil drain is on the drivers side of the engine, it's a 14mm bolt sitting on a roughly 45 degree angle towards the front of the car, you'll see it sticking out of the sump pan easily enough.
I can't say from personal experience with auto boxes, since the only time I've dealt with them is to throw them out, but the fill should probably be on the front of the transaxle, (between the engine/gearbox and the front firewall). Probably a 24mm bolt.
If it's the same as an MT transaxle, just fill it til oil comes out of the fill point

The proper place to fill the gearbox up is on front of the gearbox just below the starter motor or thereabouts, same size plug that you drained it with. You need a pump to fill it up, car needs to be level as this also happens to be how you measure if your gearbox is full.

The engine sump is the pressed steel pan, its black. Your gearbox is ally casing.

There is no dipstick for the gearbox
The only way to fill it is through the filler plug described earlier
You can connect a hose to a funnel and feed it through the engine bay to the hole, that's how I do it

Yes  Carmikey is correct.  There is a dipstick for the auto trans which you use to fill using auto transmission fluid only.   I think the other blokes missed that you are using an auto.   Often times if you let us know where you are someone may be able to give you a hand to help you  become more familiar with your car so you don't make stuffups.     It is very unlikely that the engine being a little over full would have caused any problem.

Do the autos have a separate diff section to the gearbox in the transaxle? If yes don't mix them up, they will be two completely different oils. Auto trans fill though dip stick, check level according to instruction, normally with transmission hot and engine running.

The diff if separate will generally have a drain plug and fill plug.

You could suck the excess engine oil out of the dipstick tube, saves draining too much accidentally.

Cheers