EMB-145 Captain reported a reroute and increased headwinds caused fuel reserves to drop to minimum. The reporter stated fuel gauge indications fluctuated indicating below minimums at times and FMS was not working properly. Flight crew received priority handling and landed at destination airport.

Narrative

We got rerouted from the northeast entry to the northwest entry. I estimated that we would have approximately 45 minutes reserve at the time of landing. As we progressed further westward the FMS fuel estimation for landing began to decrease. We were being directed from an area of good weather into an area of bad weather. I noticed an increase in the head winds from approximately 75 kts to approximately 125 kts at times. We were then notified that we would have to; more than likely hold. I informed air traffic control that we would be minimum fuel; and they suggested we go and divert. I used company radio to contact Dispatch. At this time we had entered the bad weather; and there was a tremendous amount of static over the radios. During the preceding portion of this flight leg; we were getting VOR fail; dme fail and GPS fail warnings along with Check reserve fuel warnings. Initially I made a mental fuel calculation based on a burn of 50 pounds per minute; and the FMS fuel balanced to the gauges. ETA plus remaining fuel figured against fuel gauges and 50 pounds per minute corroborated each other. I made contact with commercial radio and they patched me through to Dispatch. In the middle of the conversation with Dispatch before completely notifying them of our situation that we were minimum fuel; and looking to divert COM one went dead. I could not raise commercial radio after that point. At the same time; the first officer was starting a turn south; and I asked what was going on since I was off of COM two; and on COM one. I was told that they were turning us in. I looked down and noticed the FMS was stating that we had 1.0 remaining for fuel at ETA. ATC then gave us a turn westward; basically the wrong direction; and started factoring us out. I noticed the FMS quickly said 2.0 on the fuel and then quickly dropped to 0.8. 800 pounds is approximately 16 minutes and at that very moment air traffic control asked us if we needed [priority handling] and I had about five seconds to think it over at best; and I said yes. They gave us a fix; but I do not remember at this time what it was and put it into the FMS and hit direct to. The auto pilot then started a turn in the opposite direction. I turned off the auto pilot and manually flew the aircraft onto the proper course. I looked down at the FMS and at that point it was saying 2.0 for fuel. That started to confuse me as to why it was fluctuating as much as it was. I looked back down again and it was saying 0.8. Again; the FMS said DME fail; followed by vor fail. And again; for approximately the third time we received a check reserve fuel warning.Progressing toward the airport the FMS fuel estimation fluctuated up and down wildly. I was forced from the start of the event to either believe the FMS calculations; which had been accurate or to trust the fuel gauges. At that time we were out of contact with company and had no Alternate to divert to and we were in bad weather Imc. Since the FMS estimate was dropping lower each time; I opted for safety concerns to go with the most conservative of my fuel indications. I do remember looking down at the FMS fuel estimation a few times the approach. One minute it read 0.9 and then would jump up and read 2.0 and then it would go to a different number. I do remember seeing 0.3 and I was estimating that that would be about six minutes of flying time. At that time I stayed as high as possible with the power set to the lowest possible setting to conserve fuel. I did not extend flaps or gear until close in to the runway; conserving; momentum; and keeping drag at a minimum. I do remember looking for fields and roads coming into the north side of the airport just in case. The very last number that I saw on final approach was 0.3 for the fuel estimation. Upon Rollout I looked down again and the FMS was reading 2.0. Upon arriving at the gate it was either 1.8 or 1.9. Approximately. I really don't remember anything other than my hands and my knees were shaking. After we arrived at the gate; I remember looking down and it was reading 2.0 again.