Gadgeteer, bishop, lord, monk (totally worthless - they lost the stealth skill and they have no gear to make up for the lost AC), rogue and samurai. The rogue can annihilate anything with all the OP daggers but there's nothing I can do about a mage hitting my whole party for 50 damage from the extreme edge of LOS, to say nothing of the dozen other monsters that enter every fight.
I could have told you your party was terrible from the get go.
You need a Wizard, it's not called Wizardry for nothing.
A Bishop is good but it takes way too long to progress in all the magic schools and it takes a long time to get the Bishop to do anything right while the wizard has a 25% bonus on wizardry and a focus on disabling spells and aoe spells.
And if you still don't want to take a wizard, you need at least a Ranger, if you know what you're doing, because someone has to take care of the squishy wizards casting debilitating spells from behind their grunt line.
The engineer has a good ranged weapon but it only gets decent around level 15 or so, and even then, it's way behind the ranger and a triple-shot crossbow (you can get a gadgeteer's hireling, keep him until he can make it and keep him or not afterward).
Weird parties work, but rarely on your first playthrough.
On your first, you need:
Wizard, Fighter, Cleric or Bishop focused on healing (divinity) early on and at least 2 other martial characters, doesn't matter which ones, a thief, bard or ninja for disarming traps helps as well.