Use the room dividers to your advantage. You can swing your sword over a vertical room divider to get the Gremlins on the other side, even as the divider shields you from your enemy.
To keep them from throwing out food, eliminate Gremlins standing near the refrigerator as soon as possible.
If you think you can control them, let the Mogwai multiply. This gives you the potential for more points at the end of the night. But don't forget--if they eat food, they'll turn into Gremlins.
Use the flashcubes judiciously. For example, if you're surrounded by Gremlins, activate a flashcube to stun them, and then slash your way out. You can walk right through a stunned Gremlin, but if it wakes up, you'll be sorry!
You can turn on the TV and sneak up on the Mogwai and Gremlins while they're watching TV.
Time is worth more than food, so don't go out of your way to pick up pieces of food.