How can I tell who's mission is theirs without the color coding?
Most missions should be labelled with a letter e.g. M for Michael or T for Trevor. But in some cases there is a different letter e.g. L for Lamar or Lester,in these cases you would have to guess who would be the most likely character e.g. If it's Lamar go with Franklin. Hope this helps.
Edit: there is no way of telling with the strangers and freaks side quests.