Circuits with oracles vs. Turing Machines with oracles
The best reference for relativized circuits is Chris Wilson's paper "Relativized NC"  http://www.springerlink.com/content/u727654246wu8662/

The second condition you have (downward closure of O_n) is not needed to get the equivalence say between P^O and uniform poly-size circuits with oracle O. Also your third condition should be thrown away, the size of the circuit will prevent access to O_m for m larger than the circuit size.