The lever acts as a limiter. If you select L, it'll stay in first. If you select 2, it won't go above second. D allows all four gears to be used. Overdrive switches fourth gear (overdrive) on or off.
MANU makes the car stay in whatever is selected, e.g. 1, 2, or 3 (L, 2, D). The exception here is that the car won't set off in 3rd - if you have MANU on whilst in D, the car will still use 2nd gear at very low speed.
Overdrive is automatically turned off in MANU mode, e.g. there is no fourth gear in MANU. If you're driving already, it won't actually change out of fourth gear though until you hit the gas.
Red button allows you to pull out of park with the key out, or something (I have a UK car which doesn't have this.)
Taking the above into consideration, you would use Overdrive switch and the lever itself to engine brake, and also whilst flooring it out of corners or sliding so that it won't drop to a higher gear if you lift off a bit.
I never use MANU but I use the limiter a bit.