I've gt a strange relationship with JJ. On one hand I feel bad about posting nice things about him because every time Darvin complains about him I actually agree and secretly hope the devs touch him up a little. He doesn't need much, he's just the clunkiest deity - overflow issues, last chance never really being a good deal, chaos avatar whiping the XP overflow, timing issues, chaos avatar not working on below ground bosses etc...
On the other hand - I seem to use him quite a bit, and I always have ideas about unorthodox tier 2 fun crap you can do with him.
One thing he's really good for is Warlords. Gnome warlords to be precise - boost mana like there's no tommorrow, and try packing a Naga Cauldron (the early weakening and corrosion work nice with it). I had some nice Gnome Warlord + Cauldron + Rbs + Compression seal runs.
The other thing he's good for is halflings - the health boost is really good if you can make it work. Most of the debuffs don't affect spellcasters too bad in my expirience and if you're using Bloodtopowa (or are a bloodmage) it's pretty sweet. I suppose you can also go places with a Rogue.
Also, Bloodmages LOVE this guy. They generally don't have to melee stuff and still get a huge boost out of health increases. You have to find him early, though. Also, if Mysterea wasn't what she is (and that is way too good), JJ would be top choice for them.
Chaos avatar's biggest feature is knocking some resists off aboveground bosses, at least for me. If you're doing vicious runs of some sort and have to fight a resistant boss early, it's pretty good. Otherwise you run into timing and piety overflow problems. Getting rid of corrosion and weakenign in vast quantities is also a rather unique feature and works ok with Martyr wraps.
Guys who also like him are early regen fighters who manage to score a Byceps (or Byceps using wizards), since spamming Byceps like crazy increases your piety gain significantly. Spamming Wonnafyt is also fine (until everything is slowed), and combined with the health or mana increasing boons and CA (and balanced dagger

) should work for any ding! centric character (fighters, priests, whathaveyou).
Thing is, there's plenty of stuff that could work out, but he could use touching up.
I just remembered one more thing. If you plan on picking up Chaos Avatar and converting out using Pactmakers Consensus, you can probably pick a pact up. That alleviates any overflow issues and lets you get out right after you've picked the strongest boon up. I think Scholars pact (overheal and might on lvl up) might be fine if you pick CA with 90 piety, but what I generally go for these days is Spirit Pact - JJ rewards conversion, so you give it up as a source of piety but effective lower the cost of Spirit Pact. There might be other good stuff to be had with JJ + PM.
And another thing - if you're having potion problems, I feel ba... Kidding

What I mean is - try packing a keg. They're good with dwarves and elves anyway, and you can afford to blow a potion or two one the really cost-effective boosts. Another good (but circumstantial) thing is to pick the boosts when you score El Potion Loco or another subdungeon that loads you with potions. For manamonsters - Crystal Ball and Schadenfraude (and alchemist shop prep), and for healthmongers - Fire Heart (you'll be spamming for piety anyway).