Capping of TR Switch Outlet (Temp)? Two sets of wires?

So here is my problem. The tamper resistant switch outlet that was on their started making pop sounds and got very hot some of the plastic started melting off so we cut the power and cut the connections to the outlet. Before this – I had some lights flickering… Now they don't turn on at all and the outlets to the left of the outlet don't turn on.

How can I connect this to (hopefully) restore power to the affected area until the TR outlet arrives?

Any help is so appreciated