You talking about the probe end ("the probe") or the stainless braided wire sheath? Dawn & kitchen scrubber sponge works fine for me on the "probe", but the braid is another story. I think it never gets nice and shiny again.
For the thick residue I've used plain dishwashing liquid and a scrub pad. If it still won't come off, a little Easy Off might do the trick. I'd spray it on a sponge and wipe on the probe though, don't want that stuff getting into the joint where the cable joins the probe. And wear gloves.
I use Dawn dishwashing liquid and a sponge/rag , have done 4 smokes with my probes so far and seems to clean them ok. Not super shiny but at least clean.
The flexible wire close to the probes is another story, but I don't worry about that too much as I don't want to damage especially where it connects. I get it as clean as I can without putting much stress on them.
I use a dish soap and a paper towel and my finger nail if needed. I will run the cable through a damp paper towel with a little soap, but never drench it. The residue shouldn't really throw the reads off, so I don't stress over getting every spec of the stuff off of it. As long as the meat, sauce, etc is off, I'm good.
I try to clean them as soon as I pull them out of the meat.
A little Dawn and a gentle scrub.
Soak the wires and probes in lots of water? That will get you buying lots of new probe wires? Even leaving the pit probe outside in humid and foggy winters like we have here will get you spending money on pit probes?