I am currently a Level 20. Now, Everytime I killed someone or an animal, I get NO XP points. Can anybody tell me what is going on?

Level cap is twenty for base game. Thirty with Broken Steel installed.

That's as good as you can get....no more experience points for you without Broken Steel or mods.

Ok thanks, What is 'mods'?

Mods = modification packages for the game. Fan created content that is only available on the PC version, not the consoles.

There is also a console command that can change your max level. I don't know what it is, you will need to do a google search or something similar to find out what it is.

This only works on the PC, as far as I know games consoles havent developed console commands yet but I only use PC so I'm not sure.

if your playing on pc open the console type Adv.level you can level up until you run out of perks