What does strong, mild, very strong mean with respect to coffee? If you click on the coffee menu in this link: https://www.devans.in/index.php?route=common/home you will see strong, very strong, mild etc. options.

What do these options refer to in Coffee? Amount of caffeine? Amount of bitterness?
It usually refers to how long the coffe was roasted as roasting give certain taste in beans. 

So it's taste indicator. Mild is very light, sometimes called washed-down (as some places try to pass medium strength as mild by diluting it with water). It should have almost no dry aftertaste (I think you mean that by bitterness). It would also be not so acidic.
Strong coffe is the one that people usually ad milk or sugar as it most dry, acidic, and toasted taste. Brew itself will also have oily/rainbow film on surface. 

Light coffes (so mild or any that was toasted shorter than 10 minutes) have the largest amount of caffeine. But that also depend on beans type (Arabica, robusto and so on)