There is only one file type that uses the .ODEX extension:
Optimized Dalvik Executable
An ODEX file is created by the Android operating system to increase the boot speed of an Android app (an .APK file). It is located alongside an APK file and contains optimized code that speeds up the app load process.
ODEX files are the optimized versions of .DEX files, which contain the executable code for an Android app. While DEX files generically run on all Android devices, ODEX files are optimized for the specific device on which they reside. They not only help load speed, but they also decrease the amount of space required for the app.
Android creates ODEX files for apps before they are run, and they contain the same filename prefix as their corresponding APK file (e.g., MyApp.apk and MyApp.odex). The data in ODEX files replaces data used in the equivalent DEX file (classes.dex) stored inside the APK file.
NOTE: Dalvik is the name given to the virtual machine that runs the compiled code for Android apps. Therefore, an optimized DEX file, or ODEX file, is optimized for execution by the Dalvik virtual machine.
Updated: November 3, 2016