Rambo first Blood Part 2: Stallone had a custom built Hoyt Spectra bow with glass limbs and Omega wheels, which transfer the cables laterally during the power stroke, obviating the need for a cable guard.
Hoyt/Easton later released a commercial bow package based on the Spectra model (which included the Streamlight flashlight stabilizer, a custom "survival knife" with compass and necessities kit, take down arrows made by Easton, used laminated limbs and normal wheels, with a cable guard
Rambo 3: Hoyt ProVantage FPS Plus with a 90 lb. pull. I was told that they wanted a hard pull to accentuate Stallone's flexing muscles.
In the new film, I believe it is a Hoyt Matrix and a Hoyt Gamemaster in the film. Stallone requested the Gamemaster at 70# and traded for 50# limbs after a few weeks. This apparently has to do with the fact that he's expected to remain at full draw for unreasonable lengths of time during the filming process
The heads you speak of were known as 'Ripper's' made from 1956 to 1984, basically they were just polished and painted black. The exploading tips were indeed Razorback 5's painted gold for Rambo 2, and painted copper for Rambo 3. The bottoms of the cases were then filled with auto body filler, sanded down, and then painted. The box was an original box that came with the razorback's which was painted black, and then a card made up with 'Explosives' to hide the Razorback name on the top of the box.
The takedown arrows were made by Hoyt, with black feather 4" fletches. I have all of these items, in a dispaly, once i take some photos i would be willing to post them if interested? :-)