How can I remove Endermen from the game?

Yes. There are mods to completely remove Endermen and others that disable their ability to pick up blocks.

There's a built-in server command to stop the picking-up blocks portion.
Type this in the server window, if you're running the server:

gamerule mobGriefing false  

Or type this in the game chat window, if you're an op (or single-player, I believe):

/gamerule mobGriefing false  

This will also stop Creeper explosions from damaging blocks.

However, this will not remove Enderman, so there is still the noise issue.

Source: http://minecraft.gamepedia.com/Server_commands

You can also use (in the newest Minecraft snapshots) this command blocks.

You make a clock and place a command block to the side of the redstone, with this command.

/kill @e[type=Enderman]

He kills every Enderman in the game.