To remove the covers have a look at:
http://www.aximsite.com/boards/x51-h...axim-x51v.html
If I were you, I'd disconnect the LCD/digitiser and buttons from the main pcb. You can also remove the plastic battery/stylus holder with a small cross-head screwdriver. Thoroughly and carefully, wash the main PCB in distilled/de-ionised water.
Clean the LCD/digitiser with a paper towel just dampened with distilled water (don't get it soaking wet) . Pay careful attention to the contacts (they are most likely to corrode). Do the same to the button PCB.
If you have access to an air-line carefully blow the dust and excess water away from the switches, ICs etc. (careful - a high pressure blast can damage the thing)
Let everything dry slowly (e.g a couple of days) in a warm place.