I have an Elf Thief/Mage who has specialization in bows and large swords. Upon actually reading about the large swords, it says they are unusable by mages. So I thought I better roll a different character and change his specialization. But when I tried to use the sword he is able to equip one. I don't understand. Seems I should not be able to use it?

Thieves can use longswords, so a Thief/Mage combo can use them as well.

Thanks - how does one determine this? For example, even though I am a Thief/Mage, I am still unable to cast spells while in armor though, correct? So confused....

Correct. It can be a bit confusing, but basically, if one of your classes can use an item, the character can use it. So, your Thief/Mage can wear armor, but can't cast spells while wearing.

There are exceptions (such as Clerics only being able to use blunt weapons, even if multiclassed)

It's easy to get confused with all the different AD&D rules.
In the Gold Box games, using 1st Edtion rules, elf fighyer/mages or thief/mages could cast spells while wearing armour. Same with human rangers dualed to mage. But a human fighter dualed to mage could not cast spells while wearing armour.
Not excactly logical that there should be a different rule for the human fighter/mage, but I guess that's part of the charm of AD&D...
And then there is the rule about clerics only allowed to use blunt weapons, but they have the Blade Barrier spell?!?

Mage multi- and dual-class can use all armor and weapons allowed their other classes. All armor disables spell casting unless it's elven chain. Quite unlike cleric and druid multi- and dual-classes, where *that* class limits weapon use.

Nice thing about the Icewind Dale Tweak Pack at Gibberlings 3. It has a component that allows arcane spell casting, another for thieving in heavy armor (both with penalties, of course), and a third that allows multi- and dual-classed clerics and druids to use all armor and weapons of their other class(es).

Leave it to the modding community to make things a little more reasonable to fools like me.

I think you answered you question yourself.
Assuming you are playing IWD I, the user manual / character creation says [i]Elves
have a natural resistance to charm and sleep magic, possess infravision, and
are skilled in the use of the bow and long sword.[/i]
As you are a Elf Thief / Mage, he gains the ability automatically.

Race doesn't affect the weapon types you can use at all. Elves get a +1 bonus to hit with bows and long swords but if they can use them depends on class.
Pure mages don't learn how to use them, but thieves do so do any thief multiclasses except cleric/thief who refuse using pointed or bladed weapons because of religious reasons.

Basically, any class combination of cleric can only use blunt weapons.
Any class combination of mage can't cast arcane spells while wearing armor (except Elven Chain which is special).
Any class combination of thief can't use thieving abilities while wearing armor heavier than studded leather (except Elven Chain again, which is still special).

Apart from the above exceptions, all combinations gain the benefits (and usable items) of both classes. In many cases this means that they can WEAR certain items but won't be able to do certain things in them. So a fighter/mage could still switch to plate armor just fine after he's spent all his spells for the day, or if he doesn't feel like casting. And a fighter/thief can put on plate just fine if there's no locked doors or traps nearby, or if he's not feeling sneaky.