What are constructs vulnerable to?

According to the Dredmor Wiki page for Monsters, constructs such as the Unfriendly AI and Robo resist piercing, Toxic, Putrefying, and Asphyxiation damage, as well as having a decent armor absorption rating. Therefore, you're going to have to hit hard, and not rely on those damage types.

Your Promethean skill tree should come in handy, but you might want to level up your Magic Training tree so that you have more magic points and the spells cost less to cast. With 42 mana and that much magic power though, you should be able to spam Dragon's Breath pretty liberally.

With Burglary, you can lock them into place in a narrow area, blocking other monsters from pathing towards you, and then you can commence with the burnination. Staying in the ignited region does damage over time, as does being caught on fire by it.

You can try off-class weapons; the penalty is that your damage will only be 72% of what it would be normally. This might not be so bad considering the high damage resist they have against your primary weapons. Perhaps having just one "off class" weapon would be sufficient, but it will depend on the power of said weapon.