Flight Crew Last 90 Days 389; Flight Crew Type 860
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Wake Vortex Encounter
Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors
We were following other carrier's Boeing 777 for a planned seven-mile final.  The Captain had planned for a simulated AIII approach for training/currency.  The Captain was flying and we encountered some wake turbulence behind the B777; so Captain elected to fly slightly above the descent path; asked if I agreed; and I concurred. We were vectored to final; first heading 150; and asked if we had the field; which we called in sight.  Next vector was heading 220 to intercept final and cleared us the visual 24R.  The Captain stated we were slightly high due to the wake turbulence avoidance and began correcting.  The autopilot was disconnected and we began to configure.  The Captain then asked to verify AIII mode.  I went heads down; saw we weren't; and toggled to AIII.  During this time; we overshot 24R final slightly and began an immediate correction.  Simultaneously; Approach Control instructed us to fly a heading to re-intercept.  I do not remember the assigned heading.  The Captain intercepted final and the remainder of the approach and landing were uneventful. Perhaps we could have asked Approach for a slightly longer final as we remained above the 777 wake turbulence.  As Pilot Monitoring; at the critical phase of flight; I could have focused solely on the intercept to final rather than going heads down.
While the ATIS called for VFR conditions and we did have the airport in sight; it was extremely hazy. As I was transitioning my scan from the inside to the outside for the visual approach and back to the inside to check for configuration speeds; I briefly mistook Runway 24L with 24R and flew through the Localizer. I immediately corrected to re-intercept at which point the Controller called us to re-intercept from the other side. There was no conflict with other traffic that I know of.
B737-700 flight crew reported deviating from cleared track on approach to LAX. Wake vortex concerns and haze were contributing factors.