EUD stands for Extended unit Deaths. They enable you to modify bytes in StarCraft for various thigns giving you some modding capabilities and some things you can't do with modding (ie: changing a units max HP during a game, or switching weapons during a game).
Extended Alliance Status and actions for Extended Unit Deaths have been patched. You can still use EUD conditions though. A programm called uBeR@TiOn 2.0.0.9 enables you to easily utilize EUD conditions.
If you wish to use EUD actions, you must use a single player mod (I'm doing that,
). You'd have to use the 1.13a or previous starcraft.exe that will no longer work on Battle.net. uBeR@TiOn 2.0.0.7 allows you to easily utilize EUD actions, but it's not offered for downloading anymore. If you want to make a single player mod map, I'll send you uBeR@TiOn 2.0.0.7.
To sum up, you can use EUD conditions but not actions on Battle.net (conditions don't modify any ram data, so I guess Blizzard thought they were safe). Just know that Mac computers crash or disconnect when playing maps with EUD triggers.