Painting - Help! New home, horrible paint!

My husband and I just closed on our very first house yesterday. The people that owned it before us had HORRIBLE (note: horribly hideous putrid) taste in interior design and even worse painting ability! It's a modular home, and does not have dry wall, which is part of the issue.
The previous owners painted the master bedroom in a sponge paint style, which is usually quite nice if done right. Well, it wasn't. 1) They didn't start with a base coat of paint or primer. 2) they started with the lightest color. 3) They got paint on everything except the carpet and ceilings.
They painted the living room with 2 walls a dark red and 2 walls a horrible shade of dark brown. Again with the 3 conditions mentioned above.
The kitchen isn't not horrible, but, not great either. It's done in, again, sponge paint in the wrong direction (this time cream and dark peachy-orange), light on bottom, dark on top, and again, with the same 3 conditions. :madhell::wall:
My questions are...
1) Do I need to strip the paint from the walls, and if so, how do I do that?
2) What is the best way to paint modular home walls without it showing the "swirl marks" that are there?
3) What is the best way to get paint off of trim/doors/wooden fireplace mantel?
Thanks for the help in advance!

What are the walls made of if not drywall?

Generally speaking, paint can't be stripped off of walls - except for some sanding. I'm not sure I understand about the swirl marks but either sanding or skim coating over them should make the wall smooth.

Products like 'goof off' and 'oops' do a decent job of removing latex paint. There are also some solvents that will remove paint but it's best to start with the least caustic first.

It walls are the paneling type walls that are used in most moduler homes.