How do I tone down the intensity of raw onion?
Two things control the "sharpness" of onions: variety and age.  While certain varieties of onions are sharper than others (i.e. Reds, walla-walls and vidalias are sweeter), any onion which has been in storage too long is going to be sulphurous and sharp-tasting.  Since it's January now, that's going to be pretty much all onions.

Since onion sharpness comes from sulphur compounds (as I understand it), the best way to sweeten onions is to release some of them ahead of using the onion.  The best way to do that is:


Slice the onion thinly, crossways (parallel to its equator rather than pole-to-pole).
Place the sliced onion in a wide bowl, uncovered or very loosely covered, in the fridge or other cold place for at least an hour and up to a day.


Additionally, either vinegar or salt -- or both -- will help accelerate removing sharpness from onion.  For example, for a New Year's Eve appetizer this year I sliced a red onion in to rings, tossed it with 1/2 tsp salt and 2 tsp red wine vinegar, and left it in an open bowl on the 45F porch for 5 hours.  The result was intensely sweet red onion which could then be used as a canape topping.

If you're in a hurry, though, the only way to make the onion less sharp is to cook it.