Summarize:

Your taste buds only recognize five tastes: sweet, salty, bitter, sour, and savory ("Umami"). The rest is in the nose. If you can avoid smelling the food, you'll avoid a large part of the flavor. Pinch your nose as you eat or drink anything to neutralize a significant portion of the taste involved.  When the taste is truly to be avoided, take a sip of a drink before un-pinching your nose to avoid any taste left on the tongue. Slosh the liquid around your mouth for good measure. If you're eating in public or anywhere where you can't politely pinch your nose, exhale immediately before taking a bit/drink to avoid the taste. Be sure to take a small bite if doing this to avoid choking when trying to breathe again. Your taste is all about saliva. You taste different things depending on how that food reacts with the saliva in your mouth. Take a paper towel and complete dry out your mouth and tongue; this will eliminate nearly all of the taste. But remember, the saliva in your mouth is replenished every few seconds, so eat quickly after drying your mouth.  Cotton swabs such as Q-Tips are a discreet alternative to a paper towel, though you'll most likely need more than one. If you know just when you'll need to eat something unpleasant, try to refrain from having any water beforehand during the day. Drink caffeinated drinks like soda or coffee to dehydrate yourself; your mouth should be reasonably dry come time to eat. You might have noticed that any food might taste a little different depending on its temperature. Why is that? It's the same food, after all. The fact is that generally, cooling numbs your palate, toning down flavors. If you can drink a glass of cold water right before eating or drinking something unpleasant, you'll be better off. If you can chill the unpleasant food or drink, that's even better. For a more uncomfortable alternative (though preferable perhaps if you have teeth which are sensitive to cold), you can scald your tongue with a hot drink like tea, coffee, or hot chocolate. The heat will make your taste buds much less sensitive in the moments after sipping something really hot. A drink with a high alcohol concentration (such as whiskey) has the effect of a mild anesthetic on your taste centers in your mouth and nose. Try to eat or drink whatever is unpleasant quickly after drinking the alcohol for the best possible effect. If you're underage or have no access to hard alcohol, try a hygienic mouthwash which contains disinfecting alcohol such as Listerine. This too will help to numb your taste as well as distract with (usually) a strong mint flavor.
Plug your nostrils. Dry out your mouth. Drink cold water. Drink a strong alcoholic drink.