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.

No it doesnt matter what order you play them in, though if it were me, I would get frustrated playing them out of order.

After completeing them in chronological order with my origional character, I moved on to my favorite character and just did HH and OWB, but decided because LR is coming out to re-do DM, in case there happened to be additional dialogue I would miss out on.

Now I dont like to play a stupid character, I mean I've just dealt Joshua Graham and the tribes of Zion, I've out-smarted the think tank and dr mobius, but my character cant put 2+2 together and realise when he meets christina or elijah in dead money that , stuff like that niggles me, so I would play them in order, but thats not to say you cant.