How do you describe the taste of an onion?

Oniony.

It really depends on the onion and what exactly you are trying to convey to the listener. An onion might be strong, mild, aromatic, tear-inducing, acidic, salty, spicy, sweet, bitter, sour, or flavorful.

I believe that's called the "bite" or "heat" (as in spicy heat, not temperature heat).

Google Dictionary has this definition of "bite":

(2) sharp or pungent flavor.

and some synonyms: piquancy, pungency, spiciness, strong flavor, sharpness

I think the flavor of onions is "sharp." The New York Times says they are "incendiary" and that onion and garlic chemicals are "irritating," "reactive," and "stinging." The key compounds are based on sulfur, so it is technically accurate to say, "sulfury."

Onions, Garlic and Mustard has a special bity and sweet (Sharp, Piercing, Peppery, Tangy taste). Indians call it Teekha (HOT) which instead your tongue, hits straight or Kicks your nose.

Chilies and pepper do bite your tongue, but Onion, Garlic or Mustard kicks your nose and gives a burning sensation to your eyes. Onion mostly is a sugary for tongue and caramelize the food you add in. A taste maker of different kind.