This exception has to do with native libraries (JNI), and is a generic exception for "something went wrong when locating and bringing online a native library that is tied to a java library".
ELF is the default binary format for most NIX types systems (hence the .SO file extension), and the error message "Architecture word with mismatch" suggests a word is the wrong size. Some implementations make words 16, others make them 32 (usually 32-bit vs 64-bit architectures, respectively).
More than likely your java environment is being run in 64-bit mode while trying to load the 32-bit LWJGL libraries, which cannot be done.
If you're running in Eclipse, make sure to get the lwjgl64 natives for your platform (most likely lwjgl64.so), right click on your project, go to Build Path->Configure Build Path, go to Libraries, find lwjgl.jar and click the arrow on the left, look at "Native Libraries" and edit the path to the native library folder. If everything works okay, it should run.
Another thing to try (assuming regular minecraft works on your computer) is to change the native library path for lwjgl.jar in your project settings to your minecraft directory (not sure what it is on linux/mac, but on windows it's your %appdata%\.minecraft folder) and see if that works.
