Just recently tried to install an after stock radio.. After installation my newly installed radio, power outlet, turn signals and my dash lights will not turn on.

Did you use an aftermarket plug adapter or just lop off the factory plug? Did you unhook the battery before you started removal of the factory radio.

The adapter had to be spliced as the car wiring harness had no adapter and unfortunately no, I didn't unhook the battery

So you inherited someone else's hack job. You probably have another fuse box with still more blown fuses and/or wires not hooked up, not hooked up properly or loose connections. Look for wires that are just lying behind the radio not hooked to anything. Do you have a wiring schematic of your cars radio wiring? Did you at least use crimp connectors on all of your wire connections and not just twist and tape?

I replaced all fuses inside the car (there is a fuse box on the driver's and passenger's side of the car). I'm unable to see any loose wires inside the radio slot, and I'm using the old twist nd tape method. I may have connected some wires incorrectly but I can't figure out why that would knock out all of my instruments inside the car?

I used the wiring diagram for my Honda online and compared to the wiring diagram that came with the car. The wires are completely different so it took some doing.

I'm sorry, I used the wiring diagram that came with the car stereo**

Twist ntape will cause problems trust me. Once you figure out the correct way to wire it use at least crimp connectors. If you would have disconnected the battery you wouldn't have blown any fuses. Did you cut one wire at a time, a few at a time or all at once? You answered your own question "I may have connected some wires incorrectly" and that's why you have such a problem. The wiring diagram that came with the stereo needs to match up with different color wires in the dash. That's where an adaptor comes in. You connect the same color wires from the radio to the same color wires in the adaptor plug, then just plug it into the factory radio plug. Super easy to do. At this point you need to take it to either a mechanic or a stereo shop.