O Brave New World...

It was invented in Poland, so you're correct on the eastern influences. The j's have a y sound and indicate a plural when they're at the end of a word.. oj sounds like oy and indicates a plural noun (that's not in the accusative case) aj sounds like aye and indicates a plural adjective (except for the work kaj, which means "and").

The x's are not really part of the language. There are 28 letters in the alphabet, where some of these are really just letters with accents, but if you're alphabetizing, you count them separately. Unfortunately, it's really a pain in the ass to type an s with a ^ on top if you are using the US English version of mac osx. It's in unicode, but it comes out looking like: ˆs when you try to type it because apple is sometimes stupid. You have to do new keyboard mappings. Ok, so let's say you're in ascii or you're lazy and you want to type s with a ^ on top. Zamenhof, the inventor of esperanto, said to type an "sh," which is logical because it makes what sounds like "sh" in english. However, this is also stupid because 'h' exists in esperanto and has it's own sound. Also, what about h with a ^? Do you type hh? Therefore, somebody came up with a smarter solution, which is to use x. X doesn't otherwise exist in Esperanto, so there's no confusion.

pronunciation-wise:
sx = sh
hx = weird gutteral sound that doesn't exist in english, like the ch in loch
cx = ch
gx = j
ux = ow