Tell us much more please. Exactly what are the injuries? Post photos if you can.
Shock is the thing to work on first - calming the bird so it doesn't succumb. A bit of electroltyes for shock (Pedialtye or Gatorade reportedly will do in a pinch). Put the bird in a calm comfortable place so there is no added stress whatsoever. Be comforting and calm. Stay with the bird until it is calm and bright eyed and you are sure it is not succumbing to shock.
Some wounds will respond very well to cleaning and then topical application fo Neosporin (without the added pain reliever). Other times you really need to add oral or injectible antibiotic - depends on severity of the injuries.
Aspirin in water can be instrumental in pain relief (thus also helps with eating and drinking) but not while actively bleeding or if internal bleeding suspected.
Don't take the time to answer this yet - as stabilizing the bird is most important - but do you know whose dog it is? JJ