FLC OF AN MLG OVERSHOT ASSIGNED ALT AND FAILED TO FOLLOW THE CORRECT COURSE DUE TO A LAST MIN ATC ALT AND AIRSPD AMENDMENT AND THE FO'S ERROR IN SETTING THE WRONG FIX IN THE FMC.

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CLBING THROUGH FL200 WHEN CLRED TO FL280; CTR AMENDED CLRNC TO FL240 AND TOLD US TO SLOW TO 270 KTS. (WE WERE CLBING AT 320 KTS). 270 WAS ENTERED INTO THE FMC CLB PAGE. CLB RATE INCREASED TO SLOW THE ACFT. PASSING FL220 AT BETTER THAN 5000 FPM CLB RATE. CTR AGAIN AMENDED OUR CLB LIMIT TO FL220. AS WE HAD ALREADY PASSED FL220; THE ACFT PEAKED OUT AT FL230 BEFORE A DSCNT COULD BE STARTED. CONCURRENTLY; WE WERE NOW OVERHEAD SKY VOR WITH CLRNC TO WATERVILLE (VWV) VOR. DURING PREFLT; THE FO HAD MISTAKENLY ENTERED THE RTE AS SKY-VXV (VOLUNTEER) INSTEAD OF SKY-VWV. SO IN TRYING TO COMPLY WITH ATC CLRNC AND GET BACK DOWN TO FL220 AND SLOW TO 270 KTS; THE TURN S WAS NOT CAUGHT UNTIL THE ACFT HAD ROLLED OUT HEADED TO VXV. AS WE STARTED A TURN BACK TO VWV; CTR TOLD US TO TURN R TO VWV AND HANDED US OFF TO THE NEXT CTR FREQ WHO GAVE US A HDG TO INTERCEPT J-60 TO GSH. SUPPLEMENTAL INFO FROM ACN 296089: OUR RTE OF FLT WAS RADAR VECTORS UNTIL WE WERE ABLE; R-NAV DIRECT VWV VOR. VXV VOR WAS INADVERTENTLY TYPED IN THE FMC WHICH CAUSED OUR COURSE DEV. THE RAPID MULTIPLE ALT; AIRSPD; HDG CHANGES ALL CONTRIBUTED TO THE WRONG VOR BEING TYPED INTO THE FMC.