Is this possible?
I try to play Dead Money, but I don’t like it too much, so can I install and run directly the Old World Blues?

You can play the DLC in whatever order you want as long as they're installed.. you can technically even not play them, or play just a couple, they're totally separate quests with just a handle of story references between them.

I enjoy beating the DLC in a certain order:
Honest Hearts
Old World Blues
Dead Money (if I even want to play it)

I dont complete them in this order every time, but I like enjoying the DLCs in this general order.

Doesn't matter, though OWB as a new character will be extremely difficult. I speak from experience.