"Hit" can also be a correct translation of "slog".
But to somewhat arrow it down: "Slog" is "Hit" when striking someone or something with your hand or something held in your hand.
"Slog" is "Beat" when Hitting in order to hurt or soften (e.g. meat). For this meaning we have the near synonym "bankede", that can also include Kicking
"Slog" is "Hurt" if injured by an impact that equals a hit. There is a broader term that can be used for "being injured", that can be used for any kind of injury or cause: "kom til skade" (lit. "came to damage")
When a sudden thought comes to mind, you can in English say that "it hit you", and the Danish equivalent is "det slog mig" so "Slog" is also "Hit" in such case.
All of these examples are in past tense, but there is of course also a present tense variant of them.