B767 Captain reported navigation equipment issues during climb and cruise requiring the flight crew to use whiskey compass for navigation. Flight crew diverted and landed safely.

Narrative

Our flight was scheduled to fly from ZZZ to ZZZ1 on Aircraft X. We pushed back and got a clearance to taxi to Runway XX. As we taxied I mentioned that our taxi speeds looked to higher than I felt they should be. We took off of Runway XX with vectors to climb to 10000 ft. ATC the cleared us Direct ZZZ. I'm not sure of the time frame but ATC asked if we were going direct to ZZZ. We said yes and ATC said we were not going direct and we needed to fly a 275 heading. We looked at our IPad GPS course and it indeed showed us off course. We didn't have any EICAS messages or status Messages but we had an Internal Navigation and Reference System (IRS) NAV ONLY on the FMC. As we assessed the situation I had the First Officer (FO) ask for direct down the road and that we were having some NAV issues we needed to work thru. The following events might not be in the correct order as they happened but this is what I remember. After we were flying direct to the fix via a ATC assigned heading we lost our magenta navigation line. At that time I contacted the company and let them know we needed to divert due to loss of navigation. During this time after conferring with the manual found IRS Attitude. Since we lost nav we selected ATT for profile info. I don't remember if it was before or after it was selected but the Autopilot kicked off and then my and the FO's lower CRT screen blanked with no info available. The airplane started to climb and turn and I took control a flew the airplane. At that point the only thing we had for nav was the whiskey compass near the windscreen. I told the FO to contact ATC and do the [request priority handling] due to no navigation capabilities and we need to go to ZZZ2. ATC started giving us vectors and descent to ZZZ2 to a point we were able to find the runway and do a visual approach to a safe landing on Runway XYC in ZZZ2. We taxied in and parked at the Company ramp.