Air carrier Captain reported that due to the FMS and other equipment on MEL; navigation was problematic throughout the flight.

Narrative

We started the flight late due to a crewmember swap. Upon reaching the aircraft we reviewed the numerous MELs; most notably the deferred FMS and ACARS. After completing our origination checks; I noted that OXY LO PRESS Caution message and called maintenance control to defer the message for dispatch. The oxygen quantity was 1400psi and was sufficient for 2 person dispatch and was likely due to the cold temperature in the cabin at the time. The phone call and deferral; coupled with the gate agent boarding earlier than agreed put pressure on us as the crew to work quickly though the issues and complete the rest of our tasks. The FO and I briefed the route and discussed the non-standard elements of the navigation; following green needles only with no FMS to reference. We loaded the routes into our EFBs and confirmed the VOR frequencies along our route. The FO then called Clearance and they changed our clearance to be more direct from what we were initially dispatched. Clearance also queried why we were flying directly to VORs as our aircraft dispatch was listed as RNAV/GPS capable. We requested to amend our equipment identifier to exclude RNAV/GPS and only the initial 3 fixes were changed so that our clearance was ZZZ - ZZZ1 - ZZZ2 - ZZZ3 - ZZZ4 - ZZZ5 - ZZZ6.After pushing; because of inop ACARS; I had to call dispatch to confirm the manual weight and balance release and get our final takeoff numbers for the baggage and passenger load. Upon departing via runway heading; departure instructed us to turn left direct ZZZ. My FO and I both confirmed the frequency for the ZZZ VOR and neither of us could see NAV Course needles. I advised departure that we were unable to see the course and we needed radar vectors in order to proceed with positive navigation. The controller was confused but assigned us a heading and then handed us off to the center controller. When checking in with center; we advised them of the heading and no other positive NAV source and they again queried our equipment status asking what capabilities we could navigate with. We advised them of VOR/LOC/ILS only with negative GPS/RNAV/FMS capabilities. They confirmed this and then assigned another heading for our turn towards ZZZ1; which we were able to navigate to. We were then able to navigate to ZZZ2 and to ZZZ3 but then were recleared from ZZZ3 to ZZZ7 - VECTORS to ZZZ8. Upon reaching ZZZ3 we could not; again; receive positive course guidance to ZZZ7 and requested radar vectors until we reached ZZZ Approach. The reason for this report is to clarify that this flight was dispatched and routed with minimal course guidance outside of ATC Radar vectors. In the event of any type of communication failure; as a crew we would have had minimal guidance as to how to operate in terms of continuing on course. The ZZZ and ZZZ4 VORs specifically are L-VOR/DME which only provide a service volume of 70 miles and are protected up to 18;000' which we had already exceeded. The ZZZ1; ZZZ2; and ZZZ3 VORs were the only navaids that provided us with positive course navigation.