From the Phrog community perspective:
Bingo = Emergency. It's the amount of gas you need straight-line to a pre-planned airfield or the nearest airfield. There is no "profile" for us, because our gear is fixed, and we pretty much burn the same amount per engine regardless of speed or altitude.
Joker = SA builder or knock it off. Can be both, for example you plan on hearing Joker from your flight at CP B, but instead hear it at CP A - time to consider knocking it off. If you hear it at CP B, you can continue with your mission as planned. Joker can cause you to have to kick it up a notch speed wise (since our fuel burn is consistent no matter what).
Min Fuel = Not really pre-defined as an amount, but pretty much allows you to land with reserve. I've used it once. Conversation went like this:
Me: "Yuma Tower, Dagger 11 Pilot's knob inbound for runway 8"
YT: "Report the sand pits (reporting point for runway 26)"
Me: "Negative, unable - request RW 8"
YT: "Dagger 11, be advised winds are 270 at 10 - report the sandpits"
Me: "Yuma Tower, be advised I am MIN FUEL and will take the tailwind for RW 8, unless you want me to drop the big E" (that's exactly what I said)
YT: "Dagger 11 report final RW 8"
Emergency Fuel = I'm going to be landing with 200lbs/side (our minimum).
For the record - I've never used the "E" word. My co-pilot did once, and I quickly corrected it with tower (we had to land and re-arm our buckets because one didn't arm. He said we had an "electrical emergency." That was a LONG debrief for him). Two times that I could have used it: I flew into icing, and when I told them - Memphis approach gave us priority handling so no need. Lost an engine, and was so assholes and elbows in the cockpit that my dash-2 called it for me.