I have some experience with TR so mabe I can be of some help..
3 Pokemon setting up TR is a bit much. You should add a Rapid Spinner somwhere, as in my experience, TR requires quite a bit of switching.
Heres my input on your Spreads and such..:
For Jirachi, you should make it Timid with 252 Speed and HP, the reasoning behind this is simple..
The only point in Jirachi having U-Turn is to absorb the hit to safely bring something else in, if Jirachi is going to go first after you TR, then whatever you bring in will get nailed. You already have 2(for the moment) Bulky Trick Room setter-uppers, a speedy one to take a hit or 2 would be wise.
Machamp is like god in TR, not only is he slow with monsterous attack, but he is an excellent status absorber, something Ive found essential to my TR teams. Give him Toxic Orb since you already have Jirachi to heal via Wish. Payback doesnt fit very well IMO, Celebi likely wont stay in, unless it knows it can OHKO you with Psychic or something
Dusknoir seems fairly interesting although I think your mis-using him. This team is severly lacking in the defensive department. A Neutral Attack, 0 EV Shadow Punch does alot more to Azelf then a +Attack 252 EV Shadow Sneak Does, so I would swap those 2 moves. As you know, getting your Pokemon in safely is typically the biggest hurdle TR teams face, in order to help you with that, I would put Will O Wisp over EQ, as it seems to serve no purpose.
Bronzong, IMO, should go. You need a Pokemon that can function well outside of Trick Room, and Dusknoir and Jirachi seem more usefull to this team then Bronzong..in its place I would put something nice and speedy, Weavile or Swellow. Normally Id suggest a Scarf Heatran but you dont really have the defensive capabilities needed to safely switch Heatran out..
Azumarril seems to work for you so I guess i'll leave it alone.
Exxegutor is on my current TR team and works pretty good. It doesnt specialize in anything, but can do many things well, like take certain hits and setup Trick Room. While I know I said you dont need 3 TR setuppers, You need 2 Psychic Attacks even less, so Id drop Psychic for Trick Room,, making Exxegutor a little more self sufficient. Id also give it Leftovers and give it max SPatt, enough Attack to OHKO Blissey, then the rest in HP.