Though some of the nicknames i could only wish to be canon.

Midoriya= Useless Deku, Deku, Shitty nerd, Useless nerd and nerd

Todoroki= Icyhot, Cannadian Flag, Half n half bastand, dollar store elsa and prince zuko

Uraraka= Pink cheeks, round face and Gravity girl

Iida= Glasses and four eyes

Tsuyu= Frog girl and Green greninja

Kaminari= Pikachu, Pichu, sparky and dunce face

Mina= Pinky, Horns and Acid girl

Sero= Soy sauce face, creepy smile and tape boy

Kirishima= Shitty hair or Kiri