I never finished 3 and dint even play 2 but I did beat part 1 multiple times. Can I jump into this game without being confused or feeling I missed anything?
You should go back to 3 since it's one of the greatest action games of all time, but otherwise you're not going to be completely lost.
There are little nods and throwbacks in DMC4 that make more sense given some background context of DMC3, but the story is mostly self contained. No reference to anything DMC2 related, so you're safe there.