CRJ-900 Captain reported experiencing flight control and navigation issues resulting in the flight crew using standby equipment to navigate to their destination airport where they landed safely.

Narrative

During cruise flying from ZZZ1 to ZZZ we experienced an IRS2 (Inertial Reference System) failure. Subsequently; we got a YD2 (Yaw Damper) INOP status message; a PITCH FEEL FAULT status message; and the auto pilot disconnected. My FO and I ran the QRH IRS failure 11-17 checklist which prompted us to turn our ATT HDG (Attitude Heading) source selector to 1 using the remaining IRS. After that; we decided that no emergency was needed since we still had one remaining IRS and I hand flew the remainder of the flight. Rest of the flight proceeded normally until we were in the downwind of runway XXL at 4000ft. We had the localizer tuned to the correct frequency but kept getting a TRU1 (Transformer Rectifier Unit) indication in amber above the HSI. Then the localized continued to flash green then red; never stabilizing on a positive green ID. It would also not let us sequence the approach at heading XXX and was locked at an inbound course of XXX. I then proceeded to set up for a visual approach instead of the ILS because I feared the navigation was faulty. We asked for delay vectors and to set up for the visual approach into runway XXL. ATC asked us to stay at 4000 and fly heading 040. On our PFD (Primary Flight Display) we were flying 040 while setting up for the visual. ATC then called to fly 040 again which we said we were doing. On the third call ATC asked us to verify heading and we said 040 but that was when I checked the standby compass. FO and I both saw at least 20 degrees off during straight and level flight; where it said 060 on the standby compass. I then asked him to request priority hanlding as I was flying and request radar vectors to the final approach fix for a visual approach; letting ATC know we were having a navigational malfunction. I used the standby compass for the remainder of the flight. Right after ATC was advised; we got a TA followed by an RA. During that time we were 4000 feet (as we were cleared to be at) however; because we were having problems with our navigation I'm not positive we were on the right heading which could have caused the RA. I complied with the RA and then we got vectors to ZZZZZ. At this time because we were in sterile cockpit just prior to landing with traffic around us; I opted to not let passengers; flight attendants; and dispatch know about the situation because of task saturation and the desire to get the plane on the ground. I did not think it was necessary because there was no need for an evacuation and no diversions or go arounds were planned. We then proceeded to get cleared for the visual XXL. I had Papi's in sight and we descended and had a stable approach in. The green needles and heading did seem to come back to normal on final but I just used visual references to land. Emergency vehicles were waiting upon landing; however; we told them they were not necessary and taxied to the gate. Cause: The cause of the situation was the IRS failure and TRU1 indication. I believe on top of those; the heading indicator was even more off by a few degrees due to these faults.Suggestions: It would have been good to set up for a visual approach earlier knowing the navigational equipment was faulty. Also pulling up the company memo about true north indication would have been helpful and running the procedure in the memo.