Onslaught will kill bird mites, but the problem with bird mites is finding the breeding source. Onslaught may provide some relief, however many times mites will breed under carpet or in wall voids, where you cannot spray. This is why treating for mites is very difficult and usually requires multiple products and lots of vacuuming.
Each of the products you mentioned have different active ingredients, or different formulations and different manufacturers. So that we are comparing apples to apples, we will compare Onslaught and Conquer which both have the same active ingredient, Esfenvalerate and both are sold in pint size bottles. Conquer contains 3.48% of the active ingredient and Onslaught contains 6.40% of the active ingredient. You will use 1 ounce of Conquer to make 1 gallon of finished solution for flea control while you will only use .5 of Onslaught to make one finished gallon of solution for flea control. Conquer is labeled for about 50 insects, Onslaught is labeled for about 200. Onslaught also has the benefit of being micro-encapsulated which makes it safer to use indoors and makes it last longer outdoors.
Bifen is not a good choice for indoor flea control because it cannot be used over carpeting or on furniture It can only be used in cracks and crevices around the perimeter of the room. Demize EC is a great product, which offers a fast knockdown but it does not offer any residual control and it can only be used indoors.
Talstar P and Bifen IT are essentially the same product, they are just made by different manufacturers. Talstar P was manufactured 1st and is known to be the "name brand" and Bifen IT is known to be the generic. Onslaught is micro-encapsulated and will last a little longer on outdoor surfaces which does give it a bit of advantage over Talstar P or Bifen IT. You can also use either one to do a barrier treatment around the outside of your home and in your crawl space to stop pests from moving indoors.
Onslaught is a water based insecticide and you will be required to leave the treated area for as long as it takes to dry which is usually about an hour (or two hours if you were heavy handed with the spray application).
Onslaught Insecticide is labeled to be used as a broadcast spray indoors. Remove pets from the area during treatment, and once the product has dried, it is safe for animals to re-enter.