Me and my friend have made speech banks for our teams and we would like to actually be able to hear them when playing multiplayer against each other. Is it possible to install the speech banks so that we can hear it online?

Speech banks are saved in steam\steamapps\common\worms reloaded\Audio\Default\Win\CustomBanks as .xom datas. Copy these over to your friend's folder.

Kinda off, but on-topic, is there a place where you can find original Worms Armaggedon / World Party voicebanks from?

See here: http://forum.team17.co.uk/showthread.php?t=44439

Those are the only W:A/WWP speeches not included in Reloaded.