1. Whenever my cousin gets sick, she minces a bunch of garlic cloves, and then puts them on tortilla chips, puts some salsa on top, and eats it that way. Her eyes water, etc. because it's strong but at least it tastes better, and the tortilla cuts the fire a little bit. (I usually gnosh mine plain, with a few swigs of water.)
2. I think I recall one person on a forum here mentioning they put the garlic cloves in a blender with water, and then drank that. (Instead of chewing). I guess that's a good way to get a lot of garlic in your system, but chewing is what activates the garlic. If you want to try this idea, maybe put it through a garlic press, then in the blender.
3. For a tasty double-garlic dose, sometimes I first roast an entire bulb of garlic. I put some tomato pasta sauce on a whole wheat pita, toast it for a few minutes (for a dairy-free "pizza") and then top with the roasted garlic, plus several (5-6) raw minced cloves and EAT. This tastes great, isn't overly strong, but it puts more than an entire bulb (part of it raw) in the system!
Hope you find something that works for you!