Can you use a standard action maneuver, say mountain hammer, on an attack of opportunity?Could you channel a spell as a dusk blade on an attack of opportunity?
An attack of opportunity is "a single melee attack" made during the provoking opponent's turn. So, you can not use a standard action (even if that action consists of a single attack) as an AoO.
This covers both cases.
Some feats and class-skills may allow you to do this with specific spells or habilities, but the general norm is that an attack of opportunity is a single melee attack and that's that.
Also you need to have that weapon ready (i.e. in your hand) in order to do that attack (because drawing that weapon would be doing something else apart from that melee attack).