Characters can equip items from other character's inventories so long as the Inventory Glitch exists on that character. It's semi-useful in my opinion, but I don't use it in any of my runs.
The inventory glitch itself has different uses in English vs. Japanese. In the Japanese version, it can be used (iirc) to create a wrong-warp to Noah and finish off the game quickly. In the English version, you cannot do the wrong-warp, but you can still pull out every key item in the game and beat the game in under an hour (this is why Rolf's name is ABWX, as you can pull 4 of the Nei items from his name using the Inventory Glitch).
From what Jiseed told me (WR holder in Any% US and JP), the Xbox 360 version has even more options as you can use lower-case letters to name characters, so the inventory glitch opens up even more. I've been meaning to check that one out for myself.
There are a few glitches that spawn off of the main Inventory Glitch, including a Power-Up glitch that involves buying a bunch of Antidotes on a glitched inventory and the next person in line gets huge stats (for instance, if Rolf has the glitched inventory and you buy Antidotes, it will eventually override Nei's stats and she will have all her stats in the tens of thousands).
All of the important US version glitches I compiled
https://www.speedrun.com/psii/guide/r4tjj about a year ago. It explains pretty much what you need to know.