Hi there Riley, welcome to the forum. Joe's tone is complex, but achievable with pedals + at low volumes. Okay, so you say you use a Night Train. I hear they are nice sounding tube amps so you have that covered. Are you playing with single coils or humbuckers? What Joe tones are you after, his old Stratier stuff or the newer Les Paul tones? I'm assuming you are after the newer stuff, so here's what pedals I would check out:
Overdrives/Distortions: Fulltone Fulldrive II, Fulltone OCD, Ibanez TS9 or TS808 (try a BBE Green Screamer if on a budget), Fuchs Plush Creme, Ocean FX Pearl Drive, Hermida Audio Zendrive or Mosferatu, Carl Martin Hot Drive and Boost, Boss BD-2, Chandler/BK Butler Tube Driver.
Reverbs: Electro Harmonix Holy Grail, any nice Reverb tank if you can swing the $$$, Mr. Springy reverb, Fuchs Verbrator, etc. I find a nice reverb sound is KEY to the Bonamassa tone.
Delays: Boss DD-3 (what Joe uses) or DD-6, Ibanez AD-9, EH Deluxe Memory Man, MXR Carbon Copy, Line 6 DL4 or Echo Park.
So of those, I would have 1-2 good overdrives at least, one reverb, and one delay. Set the amp for a nice, slightly broken up clean that is very warm. You want to keep the treble and presense down low to avoid that icepicky tone. It's all about midrange for Joe, so I'd start at least noon on the mids. I usually have my mids on at least 3 o'clock. Adjust Bass for taste, you want some "BOOM" but not flabby mush. Now, you'll want to have one overdrive set for a crunchy Marshally plexi type rhythm tone. Try the volume just above unity (noonish) and gain to taste (also try the noon position). Think "One of These Days" intro tone. That's the riff I usually play to see if I have my rhythm tones happening. Now for the solos you'll want to just goose that sound with some gain not neccessarily distortion. I'd also roll the tone knob down on the lead pedal to back some of the highs off. Maybe try the Volume on the lead pedal for at least 3 o'clock and keep the gain below 9 o'clock. One more tip: Try using a more midrange neutral pedal for the rhythm/crunch tones and a midrange "hump" type pedal (tubescreamer) for the leads.
Okay, reverbs and delays are a lot less tricky. If your amp has a loop, and I think it does, just stick the reverb and delay through the loop with the reverb and delay at a medium setting. Joe puts all the knobs at noon on his DD-3. You don't want a cavernous sound, just a little bit of depth. This should get you pretty close...good luck and happy playing.
'67 and '74 Fender Twin Reverbs, '74 Marshall 1987 lead mkII, Metro Superlead 100. Pedals from TC Electronic, Ibanez, Dunlop, BK Butler, Electro-Harmonix, Fulltone, Maestro/Gibson, Loopmaster switching, VoodooLab, Boss. Gibson and Fender guitars, Dimarzio pickups.