EMB-145 Captain reported an electrical smell in the cockpit after takeoff resulting in an immediate return to the departure airport.

Narrative

On departure at 2000 ft. off Runway XX an electrical smell began to present itself in the flight deck and continued to get stronger. My First Officer (FO) and I donned our oxygen masks and requested priority handling. We made contact with the Flight Attendant (FA) and determined the odor was only in the flight deck. We then decided to turn back to ZZZ to make an immediate landing. The weather at ZZZ was reported 300 overcast and 1.5 miles visibility and the temps were above freezing so no deice or aircraft anti ice had been used which rules out an odor from its use. We opted for the ILS XY. Upon running the smoke checklist and heavy weight landing checklist we were cleared for ILS XY. We did fly ILS approach with autopilot but the localizer was acting very weird. The plane kept making S turns all the way down the localizer. This sometimes happens but it usually resolves itself as we get closer to the runway as the signal gets stronger. However; this time it did not and the plane continued to make s turns all the way down to minimums and eventually the autopilot failed at about 300 ft. which put the plane in an unstable state and a go around was performed. During this approach and shortly after it was very difficult to communicate clearly with ATC and other crew members due to wearing the oxygen masks with a lot of background noise and feedback. Hot mic was turned off but it was still very difficult to hear clearly. After the go around we decided to remove our masks as we noticed the odor was gone. Most likely due to performing the smoke checklist and removing the air from the flight deck. We then decided to go back to headsets and perform another approach. The second approach was similar to the first as the plane once again had trouble tracking the localizer. However; this time we were prepared for what might happen and we were able to keep the aircraft stable to an overweight landing. We were able to determine that the landing was soft enough to meet the specs of an overweight landing. We then cleared the runway and had fire rescue look over the outside of the aircraft and no defects were noted. We then taxied back to the gate and deplaned the passengers normally. The crew was pretty rattled a bit due to the nature of the priority and hard IMC conditions. We all decided it was best that we fatigued out for the remainder of the day as our adrenaline and nerves were pretty shaken and didn't feel fit to continue flying.