He starts out with Protection from Normal Missiles and Minor Globe of Invulnerability active. Based on your party setup your most secure way of taking him out is probably going to be thief traps.
As for the wands... They work a bit differently. Whether or not this is intended I don't know.
Minor Globe of Invulnerability simply makes the protected character immune to spells level 1-3. In BG1 that includes practically all of the good damaging spells. Kahrk also has a really good AC of -3 so he is quite hard to hit. He also casts Mirror Image meaning that even when he is hit his images usually absorb the blow. Non-magical ranged ammo won't work on him due to the Protection from Normal Missiles. All around he is a really tough opponent to deal with.
It's difficult to answer your question because you seem unwilling to get some "meta-game" info.
Both the normal and Imoen's wand of missile can bypass the protection in the unmodded game. Whether this is a bug or intended is another debate, let's say there is probably something wrong. Kahrk's immunities come from his items, specifically two of them + another non protective feature. They correspond with well known spells. Not sure about what is logged in the combat log but you should be able to identify all of them graphically. He can renew one of them by casting a spell, in addition to the mirror image he is likely to cast at the beginning of the fight. He is a lvl 12 mage unable to cast spells granted at this level but he has weird not to say illegal saving throws even though it is always difficult to estimate what the dev/author wanted to simulate.
Haste Minor Globe of Invulnerability Protection from normal missiles
He can recast the globe
The SCS flavor is rather different, reenabling his spellcasting capabilities and making him legit. However the main difference comes from the very effective Fighter/Mage script he runs.
Thank you for the informative responses. I'm not avoiding meta-game info, just trying to play my party as though they aren't aware. I knew that not having dispel magic available or ready would make this fight more interesting/challenging.
Dispel Magic is unlikely to succeed because of the difference of levels and it would not dispel the globe anyway. Your team may not know the former (in a fairplay game) but they are "allowed" to know the latter. The decision to cast the spell would be made semi-blindly as you may still dispel other enchantments despite the globe. However other spells attacking this globe such as spell thrust or secret word would be effective.
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As for the wands... They work a bit differently. Whether or not this is intended I don't know.
Both the normal and Imoen's wand of missile can bypass the protection in the unmodded game.
Whether this is a bug or intended is another debate, let's say there is probably something wrong.
Kahrk's immunities come from his items, specifically two of them + another non protective feature. They correspond with well known spells. Not sure about what is logged in the combat log but you should be able to identify all of them graphically. He can renew one of them by casting a spell, in addition to the mirror image he is likely to cast at the beginning of the fight.
He is a lvl 12 mage unable to cast spells granted at this level but he has weird not to say illegal saving throws even though it is always difficult to estimate what the dev/author wanted to simulate.
Minor Globe of Invulnerability
Protection from normal missiles
He can recast the globe
The SCS flavor is rather different, reenabling his spellcasting capabilities and making him legit. However the main difference comes from the very effective Fighter/Mage script he runs.
Edit: added spoiler
However other spells attacking this globe such as spell thrust or secret word would be effective.