Last Night on Earth is kind of a lighter game in terms of strategy. There are different scenarios you can play, but most of them require you to march around the map and visit different buildings in an attempt to get better items. IIRC the items are drawn randomly from the deck or depending on what building you are in you can search the discard pile for a fairly specific item (usually a weapon.)
Combat is relatively simple. You need a weapon to kill a zombie, otherwise you simply push it away. Some weapons are better than others. Usually better weapons are better because of how many dice you can roll which increases your probability of getting a hit. With regard to fire arms you can run out of ammo depending on what you roll, and some weapons are more prone to run out of ammo, so using your weapon can be tense (you don't want to run out of ammo - in which case you simply discard the weapon) but generally using a weapon is advised. Your melee weapons can also break.
The characters are varied but are pretty stereotypical of horror movies (the jock, the prom queen, the cop, the priest, etc.) Each character has their own special abilities.
I guess a big part of the strategy would be the card play. Each player gets cards that they can play which can do various things such as allow them to move more spaces, roll extra dice, get a weapon, etc. The Zombie player has some truly nefarious cards allowing him to play more zombies, let zombies move farther, etc. One card the zombie player can get is the titular card "last night on earth" which is played on a female character and a male character in the same space on the board. They lose their turn because they are to occupied doing, uh, other things...cuz it's the last night on earth and all
What I like about this game is that basically the Zombies never go away. Most of the scenarios rely on you defending for a certain amount of turns or on escaping the town (in one scenario you have to fined the car keys, a can of gas, and then get to the truck with at least one person). There is a maximum amount of zombies that can be out at any given time, and some turns there will be less zombies - but there are always zombies.
I think evading the zombie thread and seeing the looming horde of the undead is a fun aspect of the game. Basically this is a game that you probably want to play with friends who like zombie stuff and can really get in to the game. Probably wouldn't hurt to have a few beers either.
