This.
That guitar could have been sitting around with those strings for months or even ears depend on the manufacture date. having them just sit around, even unused, and probably going through many different humidity and temperature changes through shipping, can cause them to be really unpredictable.
When your sure the tuning pegs are tight (you have to take the strings off to really tell, or at last loosen them, because the tension of the strings can make them appear tight), and you have a new fresh set of strings on, and still having problems, it comes down pretty much to the nut.
Do as previously said, and shave some graphite from a pencil into the slots of the nut it'll help the strings flow through the nut without getting caught. (Never tried vasoline but I'm sure it'd work, but graphite is a pretty common convention).
The thing I usually do with a new guitar, is try to slightly file the sides of the nut. I always find that they are cut slightly tight. I like to open them up, not so much that the string can move around in the nut, but just to slightly give it a bit of room. The way I usually do this, is the first set of string I put on the guitar, I usually go a size up for gauge from the normal strings I like.
ie - I play 10-52, but I put something heavier, I think last time I used 11-58 or 11-60. Played those strings for about two weeks then put the normal ones I play on.
Cheers and good luck!