At 8 AWG you could use a small split bolt type connector (assuming you have room, they're a bit bulky). See McMaster-Carr http://www.mcmaster.com
or your local electrical wholesaler. Insert the three wires, wrench it down tight & wrap it in vinyl (3M/Scotch #33+ or #88) electrical tape, and/or silicone or EPR self-fusing splicing tape (e.g. 3M/Scotch #23, #70, etc.).
As you say, offset the splices slightly, taping each, and tape or tie-wrap the pair if desired.
Soldering and taping or heat-shrinking (including heat-shrinks w/ a melting/encapsulating lining) are another option, but at 3*8 AWG, you're in sizes that are difficult to solder well, but if you have a big soldering iron or soldering copper, is successful, would be more streamlined than split bolts. I don't think I'd attempt soldering much bigger than 3*12 AWG, but if you do, be sure the junction's mechanically sound/strong prior to soldering.
Another option -- if you can: make one run *full* length (source to load), strip a region in the middle of the run, where you need the branch to leave, and solder the branch to the uncut wire (then it looks like a joint of only 2 not 3 10 AWG wires), and seat-shrink or tape that. Initially the branch will leave at 90 degrees (in a T) but you can bend it parallel to the existing wire before soldering if desired.