Are class levels kept when under the effect of PAO?

[Frostthehero]

That is, would a wizard who casts polymorph any object on himself still be able to cast as a wizard of the same level?

[Zanos]

This spell functions like polymorph,

This spell functions like alter self,

Your class and level, hit points, alignment, base attack bonus, and base save bonuses all remain the same.
As long as there is no contradiction, you follow the chain down to alter self. So yes.

[Psyren]

Keep in mind though, OP, that your exact question was "would still be able to cast." While you'll certainly keep your casting ability/training, you can if not careful easily polymorph yourself into a form that isn't capable of providing verbal or somatic components (or both) and get stuck that way.

(PAO can also duplicate the effects of baleful polymorph, but one presumes you weren't planning to use that particular function on yourself.)

[Mr Adventurer]

Also remember equipment tends to be either absorbed or dropped - so watch out for your material components too.

[Zanos]

That's why you should prefer humanoid(shape, not type) forms that are capable of speech. Avoids the spell component and equipment issues. Fortunately, many high intelligence forms come with the good old 2 arms 2 legs and a head configuration. Higher HD outsiders, Ethergaunts, and Sarrukhs are all good choices.