How can I replace the word 'later' (as in 'two days later')? Can I say 'two days on'? Doesn't sound right, but I heard 'on' being used in the meaning "further in time".
Not "two days on". You could have "two days later on".
There is no real reason not to use later. I suppose you could say "two days after that" (where "that" refers to some event previously mentioned)
The first earthquake was on Monday and one day later smoke was seen rising from the volcano's crater. Two days after that, a powerful eruption blew out the side of the mountain.