I'm in Dragoon's Caverns, and I hate these guys. My Knight is useless, my Cleric is useless, and my Archer can do a bit of damage of Static Charge but quickly runs out of mana and becomes useless. My Sorcerer can do a bit of damage with Fire Arrow, and has plenty of mana for it, but it still takes forever to kill anything and all the while the oozes are pounding my party, poisoning them and breaking their equipment.

I'm guessing I'll need some direct-damage elemental spells, but what can I get at this point of the game? My party is at level 7, and I've visted New Sorpigal, Castle Ironfist, and Mist.

My sorcerer is a fire expert, and is level 1 at the other elementals. My archer is level 1 at all elementals. My cleric is a body expert and is level 1 mind and spirit, but I assume that won't help at all.

Honestly I have no idea what the effect of non-elemental magical damage is on oozes, since I've always used cleric casters to cure poison. But even starting out your archer should be able to cast ring of fire at least once, if not twice. At character level 7, with expert skill level, this'll be your best spell for damage and economy.

It's also a bit cheap, since you can use it to attack enemies that cannot attack you (it kills in an area around your characters, even through walls). Fire bolt is the next best, since it doesn't cost much but does more damage (though only to one creature) than fire arrow.

Anything better will burn up your sp before it does any good until you are a few levels higher.

Additionally, to make your non-casting characters less useless, you can equip them with spell scrolls.

I agree with Thiev. The cave is obviously too hard and painful for your party now, leave it and return when you are higher level, better equipped and have more spellpoints.
There are so many other locations where you could go first.

Not really, you can easily finish all you really need to do in Dragoon Caverns and leave the Oozes for later. Just don't fall in that dungeon's sewers.

>>>Honestly I have no idea what the effect of non-elemental magical damage is on oozes, since I've always used cleric casters to cure poison

Oozes only take damage from Fire, Electricity, and Ice elemental. And Energy, of course, (nothing in the game has resistance to energy elemental) . They're immune to Poison, "Magic" element, and physical.

BTW, Moon Ray is Energy elemental, but too bad it doesn't work inside.
Try it sometimes, it does always full damage to Titans, Undead, wind elementals, gold dragons, etc

So, nothing in the Earth spell school can damage Oozes (every spell except Mass Distortion deals physical damage, Mass Distortion is magic elemental)

A Cleric, even with all spells learned, is completely worthless against Oozes. All self-schools damage spells deal magic elemental damage. Dark spells are either poison, physical, or magical (Armageddon is magical), Prismatic Light is magical. Sun Ray is fire elemental, but you never encounter Oozes outside.

"Of the Dragon" enchantment is also Energy elemental due to a bug. So you can kill the reactor with Of the Dragon weapons and never enter the Control Center at all. But I consider that cheating.

I have played several clerical-only games, and without a sorcerer or druid, by far the best option vs Oozes are :
1) Wands of Fireballs
2) Wands of Sparks
3) Fire, Lightning, or Ice enchantments on weapons. Since those are very rare early in the game, I suggest stocking up on the aformentioned wands whenever you can.
4) Wands of Ice and Wands of Fire will also do nicely.

I don't bother buying Wands of Cold, Wands of Static, or Wands of Flame as those are just too weak, but I'll keep them if I come across them in chests.