An unseen servant is an invisible, mindless, shapeless force that performs simple tasks at your command. It can run and fetch things, open unstuck doors, and hold chairs, as well as clean and mend. The servant can perform only one activity at a time, but it repeats the same activity over and over again if told to do so as long as you remain within range. It can open only normal doors, drawers, lids, and the like. It has an effective Strength score of 2 (so it can lift 20 pounds or drag 100 pounds). It can trigger traps and such, but it can exert only 20 pounds of force, which is not enough to activate certain pressure plates and other devices. It can’t perform any task that requires a skill check with a DC higher than 10 or that requires a check using a skill that can’t be used untrained. Its speed is 15 feet.
Can I send the servant into the air above my head, or above the head of enemies?
Yes, because it's a "force" (not a creature)
The key word here is Force. An unseen servant is not in the same class as, say, an incorporeal being under greater invisibility. It is, rather, a spell-created force effect that the caster controls via commands...rather like a simple automaton.
As a spell-created force-effect, it doesn't truly have any "movement type" at all -- rather, it merely has a speed which determines how quickly it can move from one place to another.
Unseen Servant can be thought of Mage Hand, Programmable Edition. It can do anything anywhere anyhow, so long as it is within the parameters of the spell...and by this, that includes flying.
By the way, as a total side note, if you play something that can get your own weight under 20 lbs though Reduce Person or other means, your Unseen Servant can carry you, too, as it flies about.