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In case it wasn't clear, Oozemancers start out as Zigur followers, and are unable to use any Arcane items.
Oozemancer is one of the most powerful classes through most of the game. Slime Spit clears most of the monsters that can appear around levels 1-3. Poisonous Spores can kill most early bosses with a single casting. Later on, Living Mucus will provide minions that act as distractions and spotters.
Oozemancer has 2 strong defense mechanisms. Antimagic Shield scales with Mindpower, excess Equilibrium will be very quickly reduced by mucus. Mitosis itself is nearly meaningless, but coupled with Call of the Ooze and Reabsorb, it rivals Solipsist's Dismissal and Mindslayer's shields.
Thanks to Poisonous spores, Mucus and Acid Splash, Oozemancers can destroy almost all living monsters (even the overleveled vault ones) within a few rounds. It's nothing unusual to clear an entire room of orcs with just one casting of either spores or acid splash.
This leaves the much more problematic undead and constructs. Most of those can't heal very well and so can be worn down rather easily - Fungus tree will ensure constant regeneration, making an Oozemancer a king of sustainability. Poison resistant rares with lots of hp and means of regeneration can't be easily killed and might require multiple retries. Archmage rares can often be stripped of their healing and escape spells (and all other for that matter) by repeatedly Mana Clashing them.
There is one status to which Oozemancers are particularly weak - stunning. Most other common effects are covered by their Indiscernible Anatomy. There is nothing wrong with having your starting wild infusion during the final boss fight, as Oozemancers don't need many infusion slots.
The best race for Oozemancer is probably Thalore. Their active damage/resistance bonus scales with Willpower, of which you'll have a lot, the passive resistance will help reach the resistance cap when using Reabsorb, and summoned treants will make perfect meatshields in an emergency (when all other allies die, for example).
Halfling's racial abilities will not synergize as well. Oozemancers will want a passive crit rate near 100%, have no need for high saves (on normal difficulty), are unlikely to be surrounded or in melee with dangerous enemies and will want a passive stun immunity in late game.
Yeeks' immunity to confusion will be wasted on an Oozemancer. All Oozemancer's defenses require some hp buffer, meaning they can't be used well without a high hp pool.