Your wiring reminds me of my own system. I have an older house that did not have central air conditioning when built. Later when A/C was added, they ran an extra 2-wire thermostat line and changed out the thermostat for a model that supported heat and cooling. It looks like in your situation they cheaped out and just used stranded speaker wire for those extra 2 connections instead of the proper smaller-gauge solid wire. The heavier stranded wire will not fit into the Nest terminal connectors. But you can make this work simply by adding some short 4"-6" pigtails with smaller gauge solid wire. Just attach them to the stranded wires with wire nuts and shove that part back into the wall, leaving just the solid pigtails coming through to connect to the Nest.
The photo is confusing, because one of the speaker wires connects to 'C' and it looks like the other connection is to R. Then you have a red wire going to Rc which is jumpered to R as well. It would appear that either the extra speaker wire going to R or the red wire going to Rc is redundant. Or you might have something unusual in the setup there. If it were me, I'd pull the door off the furnace to see where that extra speaker wire and the red wire are going.
