Eh, actually Umbreon is resistant to Ghost. Just sayin'.
On the Current Topic:
If you give Umbreon Leftovers, the opposing Pokemon won't be able to do much to Umbreon before it faints the opponent Pokemon (Some Umbreons use Toxic, while others are Elemental Fighters). Umbreons can be very hard to defeat if you know what moves to teach it, and PLUS it has Synchronise which makes some Status Problems affect the Opposing Pokemon. Stack that with Confuse Ray, then you need to do little to win a battle. Which means, despite Umbreon not being very fast, it can take down the enemy with almost any Status Problems (Except a couple such as Burn). Plus it is only weak to Bug (Which is very weak anyway, so Umbreon would take it down easily) and Fighting (But Umbreon has Psychic in it's Move-Pool, so it doesn't matter). Plus the way of getting (Try not to take it the wrong way) Umbreon is PROBABLY the most challenging (Since you wouldn't be up at night). Remember, Umbreon also has a good Move-Pool (With Iron Tail), as said before. Umbreon will serve as a good Pokemon on anybody's team, but only if they know how to use it.
That's all I got to say for now.