The gamey taste in venison can be due to a variety of reasons. One factor is diet. Another factor is how quickly the deer was killed. These previous two points have already been posted and I agree with their arguments.
The following point has been mentioned but not defended. The major factor is how the deer was handled after it was killed. The meat needs to be cooled quickly after the kill. Letting a deer hang for over ten hours in 60ºF or higher temp is a good way to get that gamey taste. You wouldn't let a hog or beef side hang overnight in warm weather after gutting it, why would you do this to a deer?
Deer fat will also have a gamey flavor. Trim all of this from the meat that you can. There isn't much fat on the back strap like there is on the hams and to a lesser extent, the shoulders, so this shouldn't be a problem. Make sure you trim all the silver skin you can from the outside of the loin roast. This is best done by getting the meat almost frozen and using a very sharp knife to remove the skin. This trick will keep you from cutting too much meat off the roast. This silver skin that surrounds muscle groups can be very tough. One of the thicker membranes is on the back strap.
I have had good success with this recipe that Qsis posted on the BBQ Forum years ago:
http://www.bbqsearch.com/bbqboard/displayMessage.asp?id=192787&keywords=marinade
If I am using the recipe as a marinade, I follow the ingredients to the letter. You can marinate the roasts or steaks for as long as overnight.
When I use this recipe as an injection solution, I omit the vegetable oil. I make up the solution a day or two in advance so the flavors can meld. I then strain the solution so that the garlic, pepper and parsley do not clog the injecting needle. I use about an ounce of solution per pound of meat and let the meat rest for about four hours before cooking.
Reserve some of the solution for later. The rub I use on venison is a combination of brisket rub and Montreal Steak Seasoning.
One thing you do not want to do with either steaks or roasts is over cook the meat. Venison is best served medium rare or medium at its highest temperature. Anything over 155ºF is going to be dry and possibly chewy. If I am cooking slow, I will remove the roast at 145º. On a fast cook, I will remove the roast at 140º. The roast gets wrapped in foil and rest for about 20 minutes before slicing. Remember that reserved marinade? Heat some of this up and pour it into the foil before sealing it.
I hope this helps and if you have any questions feel free to ask.
Lager,
Juggy