"irgend-" corresponds pretty much straight on with "any," such as anybody, -where, -thing, -time, and "any" itself. That's also the difference, and you can use any... pretty much the same way as "irgend...," as long as the sentence isn't used in the negative. That's when it changes.

Does that answer your question somewhat?

My question isn't with the prefix, it's more with the word 'irgendwer' in relation to the word 'jemand'. The both can mean 'someone', am I right? In what situations would you use one over the other?

"irgendwer" often has a stronger connotation of "It doesn't matter who" or "I don't care who" or "It is not important (to me) who", than "jemand" does. Often, not always.

You can often interchange the two but depending on context and tone you wouldn't.

For example:
"Jemand hat die Tür aufgelassen" is quite interchangeable with "Irgendwer hat die Tür aufgelassen".

But

"Kann bitte mal jemand die Tür zumachen" is a politely worded request, whereas "Kann mal irgendwer die Tür zumachen" would indicate a thought in the back of the speaker's head of the kind "I don't care who, just shut that door, I'm bloody freezing".

Hope that helps ... maybe somebody comes up with a better way to explain it.

Ah. Ok. That makes sense.

In the first sentence you used "bitte", but not in the second. Could you use it in the second sentence as well? Would that sound more polite or just awkward?

Thank you for your help. :]

Gefühlter Unterschied!!!
"Jemand" zielt noch auf eine bestimmte Gruppe, während "irgendwer" da ganz offen ist.
"Irgendwer wird sich schon finden, der hier aufräumt".
"Kann mal jemand hier aufräumen?"

@Vikki: Yes you could put a "bitte" in the second sentence, too; it would not sound awkward. If it comes across more politely though would totally depend on the speaker's tone.