ACFT NAV SYS BECAME UNRELIABLE. FLC DIVERTS TO VFR ARPT.

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SOMEWHERE E OF LVS; WE WERE CLRED TO FLY DIRECT RNAV TO ILC. OUR FMS HAD BEEN ACCURATE UP TO AROUND FMN. ABOUT 100-150 DME W OF FMN; CTR CALLED TO ASK IF WE WERE STILL ON AN ASSIGNED HDG. I REPLIED THAT WE WERE NOT ON A HDG; BUT FLYING DIRECT TO ILC. WE WERE THEN TOLD WE WERE OFF COURSE AND TO TURN 20 DEGS R. WE COMPLIED AND BEGAN TO CHK THE STATUS OF OUR FMS. THE 'VERIFY POS' MESSAGE APPEARED AND IT BECAME EVIDENT THAT THE FMS HAD LOST ITS ALIGNMENT. THE AUTO WINDOW OF THE VOR FLASHED 108.0; MEANING IT COULD NOT FIND A STATION FROM WHICH TO GET A FIX. WE WERE GIVEN A TURN ANOTHER 15 DEGS R. WE CONSULTED OUR NEW OPS MANUALS. THE QRH HAD NO PROC. THE OPS MANUAL; VOLUME 2; HAD A BRIEF DESCRIPTION OF WHAT TO DO FOR A LOSS OF ALIGNMENT. IT INVOLVED SELECTING 'ATT' MODE ON THE IRS PANEL AND ENTERING HDG MANUALLY. AFTER ANOTHER 40 DEG TURN TO THE R; THE COPLT STATED THAT THE HDG WAS 'WAY OFF.' IT APPEARED TO ME THAT HE WAS RIGHT. WE DISCUSSED SELECTING 'ATT.' WE SELECTED 'ATT' ON THE IRS AND PROMPTLY LOST THE AUTOPLT AND THE RDMI AND HSI. THE COPLT THEN MANUALLY FLEW AND TALKED ON THE RADIO WHILE I CONTACTED THE DISPATCHER. THE DUTY PLT WAS NOT AVAILABLE; SO WE TALKED WITH THE MAINT COORDINATOR. HE SUGGESTED PULLING AND RESETTING SEVERAL CIRCUIT BREAKERS. WE DID THIS AND TEMPORARILY LOST THE ADI. WHEN I GOT THE ADI BACK; I DISCONTINUED THE 'HELP' OF MAINT. OUR DEST; OAK; WAS IFR; SO I REQUESTED A DIVERT TO A VMC FIELD AND VECTORS TO REMAIN IN VMC TO LNDG. THIS WAS GRANTED AND WE LANDED IN SLC UNEVENTFULLY. CONCLUSIONS: THE TRAINING ON THE IRS AND THE FMS IS VERY LIMITED AND USUALLY ONLY DONE AT THE INITIAL SCHOOL. WE JUST CONVERTED TO NEW MANUALS AND HAVE NOT YET BEEN FULLY TRAINED IN THEIR USE. AS CAPT; I COULD HAVE TAKEN MORE TIME TO ASSESS THE SIT BEFORE ACTING. THE DECISION TO DIVERT TO A VFR FIELD I FELT WAS A GOOD ONE.