Loli (short for lolicon) is the sexualizing of little girls. This can be anywhere from actually showing them engaging in sexual acts to just appearing in a way that, if they were older, be considered tantalizing to men. There is also shota, which is the same thing, but with little boys instead of little girls.
I can't really give you a suggestion of a show that has this since I don't watch this kind of garbage, but just imagine if Renge from Non Non Biyori was placed into an H-game, that's loli.
Moe is kind of like lolicon, but adolescent girls. You find this in a lot of anime and even more in Japanese RPGs. Beyond just hypersexualizing barely pubescent girls, it is also used as a term to describe when girls are done in an overly "cute" way in how they dress, do their hair, etc.
K-On! would be an example of moe.
Kawaii literally just means cute/adorable, anything can be this.
I think Nu Gundam is kawaii.