B737 Captain reported a navigational error accompanied by a wake turbulence encounter. The Captain states the crew did not notice the FMC's had sequenced to the next leg; causing them to select an incorrect waypoint. Once on the incorrect heading the Captain was behind a heavy 777 and encountered wake turbulence.

Narrative

Prior to TO (Takeoff) we were told to turn left at shoreline heading 210; we complied with clearance when we switched to LA Dept while on heading of 210 and fairly abeam SHAEF we were told to go direct to PEVEE; at this point SHAEF was on L1 and PEVEE at L2 so when we got the clearance and FO was going to select PEVEE; we passed SHAEF then PEVEEE was at L1 and HOLTZ at L2 so accidently HOLTZ was selected instead of PEVEE and LNAV took us that way. At the same time I encountered wake turbulence since we took off behind a heavy 777; I started to get the wake and while paying attention to my attitude and altitude and I was distracted to confirm PEVEE so since we were going to HOLTZ it took us closer to the coast which we needed to avoid for noise; we did not get over the land; shortly after established to HOLTZ Departure called and asked if we are going to PEVEE and that is when both me and FO (First Officer) realized that we were headed to HOLTZ; we corrected immediately and back towards PEVEE; since I was focused on flying the airplane caused by wake I missed to verification of PEVEE in the FMC and MFD. At no time where we in close proximity of any aircraft our error was lack of verification of fix and confirmation.