This is a fairly "common" issue, that typically occurs due to high resistance at the terminal. The high resistance can be caused by corrosion, or a loose connection. The high resistance causes heating, which causes higher resistance, which leads to more heating. Eventually the insulation on the wire starts to melt, and/or burn. Usually the heat will transfer through the terminal block, and into the smaller wiring in the stove. When the heat becomes too much, the smaller appliance wiring will fail and open the circuit.
In most cases this is not a super dangerous event, as the wiring is contained within the stove. However, there is a chance that this can lead to a fire in the house, especially if the cover is not properly installed.
Causes
Corrosion
Corrosion is more commonly a problem if the wiring is aluminium, though can still be a problem with copper wiring. Because stoves/cooktops/ranges draw large amounts of current, there is typically some heating of the wiring during operation. The constant heating and cooling cycles of the wiring can lead to corrosion, and/or hardening of the wiring over time. This corrosion and/or hardening increases the resistance of the wiring, which cause the heating to be worse.
Solution
Occasional inspection of the terminal block and wiring, can prevent the corrosion/hardening from getting too bad. If you notice any discoloration or corrosion, have the cord replaced. There are also conductive pastes available, that can be applied to the wiring and terminals to help prevent corrosion. While this should always be used with aluminium wiring, it may also be applied to copper wiring.
Loose Connections
This can be caused initially by not tightening the terminals to the proper torque (usually specified by the manufacturer), or over time by heating/cooling cycles. Loose or bad connections can cause arcing and/or higher resistance. As discussed before, high resistance leads to heat.
Solution
Make sure all terminals are tightened to the manufacturers specifications. It's also a good idea to tighten the terminals after a few hours of operation. As stated before, occasional inspection can also prevent this situation.
Why didn't the breaker trip?
The heating was localized to the stove\cooktop\range, so the thermal protection in the breaker would not trip. Since stoves\cooktops\ranges draw large amounts of current during normal operation, the current during the event likely didn't go high enough to cause heating in the breaker to trigger the thermal protection. It could also be that the breaker is faulty, so it should be inspected.
Is the stove scrap?
The stove may be salvageable, though you'll want to thoroughly inspect all the wiring to insure it is not damaged. Replace any damaged wiring with equivalent parts (cooking appliances use high heat resistant wiring).
If the stove is still under warranty, you'll want to contact the manufacturer to discuss your options.
Both of the things you report - the smell and the hum - are very likely indications of a bad connection or bad contact in the disconnect.
Bad connections and bad contacts generate heat, the heat can damage the insulation of the wires, and even cause a fire.
I'd leave that disconnect off and if possible turn of the breaker for the circuit until it can be checked. You'll probably wind up having the disconnect replaced, hopefully the wiring can be re-terminated without replacing it.
Best Answer
The plug metaphor doesn't work, because these loads are quite large. 50A circuits can't have 2 outlets. EVSE's can't share circuits. And a 50A appliance needs a 50A breaker to protect it from internal shorts -- if it had a 90A internal short, the 100A breaker wouldn't protect it!
The circuit breaker must match the load(s).
As discussed, each EVSE must have a circuit breaker dedicated to it, and the breaker must be the appropriate size for the EVSE according to its specs and docs. Chevy Volts either use a Level 1 13A/120V charger... or a Level 2 32A/240V charger. Neither of those wants a 50A breaker. Hot-dogging this stuff is not appropriate.
You're always allowed to use a larger wire than is required, so a #4 wire on a 20A circuit is absolutely fine, provided the breaker is 20A and the socket is 20A.
The breaker must protect the wire. (and the loads).
The largest breaker you can use is decided by the wire. We have tables for that, namely 310.15(B)(16). That is based on wire size, wire type (indicating temperature allowed, 60C vs 75C), and copper vs aluminum.
For instance #4 aluminum THWN-2 in conduit is allowed 65A, which you can round up to a 70A breaker.
However, still, the breaker is also limited by the load; e.g. a Level 2 Chevy Volt charger needs a 40A breaker.
The reason is the 125% derate required for EVSEs and other continuous loads. You must provision 125% of the actual current draw. That is why the Volt Level 2 charger is 32A. 125% of 32A is 40A, a common breaker size.
Subpanel is how you solve this.
You can run the wire right up to its 310.15(b)(16) limit if you have it feed a subpanel. Then, in the subpanel, you install breakers appropriate for each EVSE.
We recommend lots and lots of spaces in the subpanel, because spaces are cheap, and running out of spaces is a stupid, expensive problem. So you take our advice and get a 16-space panel with 125A busing. Take that 70A example. That's more than 70A so that's fine.
Then, you install breakers. You install a 40A/240V breaker for your existing Chevy Volt Level 2 EVSE, and a 20A/120V breaker for your level 1 EVSE and general tools. You get the Tesla, and it wants a 50A/240V breaker, so you fit that also.
Now, the 70A breaker in the main panel protects the #4Al wire in the walls, and also protects the 125A busing in the subpanel. Each EVSE breaker protects its individual EVSE.