the YJMs and HS3 are stacked 'buckers and dont hum.
there really are million different things that cause hum, from poor wiring inside the guitar, to bad shielding inside the guitar. I assume if your using YJMs and HS3's its on a strat or strat style guitar. take the strings off, take off the pickgaurd and look to see if theres any bad wiring. Everything should be neat and clean, with the proper use of shrink tubing, and the whole inside of the pickup cavitys and the bottom of the pickgaurd should be covered in what looks like aluminum foil (its actually shielding, to block stray EM fields.) the pickups should be wired correctly, in series and in phase with each other.
Take the covers off the pickups and look at the windings on the bobbin, it should be clean and no loose copper wires should be sticking out. next, check your 5 way, is it loose? scratchy? might need cleaning or replacement. also check your Pots for the same thing (volume and tone knobs)
Next check your Input jack for the same thing. Strats are prone to loose input jacks.
Also, before you take the stings off, put your guitar down, dont touch it, turn everything on and volume up, does it hum? now, touch the strings, and also touch the jack area, does the hum change or cancel out? if so, you might have a bad ground somewhere in the guitar.
A bad wiring job inside the guitar can mean WORLDS of difference in tone and sound.
if everything checks out OK, it might be your pedal, ive never personally used a Boss OD3, so I cant say if it is or isnt noisy. I would suggest, if you like the 1 OD pedal into a amp, I would recommend trying a Ibanez TS808 or similar reissue Tube Screamer, its pritty much the industry standard shred/metal OD pedal for the last, oh I dunno, 35 years..
well, thats all I can think of for now...
oh, and a noise gate is a electronic device that constantly measures the signal for input, if there is no input, it cuts off the signal, killing any noise, as soon as there is a signal, it opens back up, and this all happens in milliseconds. EVERY guitar player should, wait no, NEEDS to have one. Most new guitar toys like POD and others have them built right in (the POD has actually a very nice one, I was impressed by it after using stuff like Rocktron HUSH, and compressor gate rack systems. Yngwie actually 2 seperate gates in his system.