Ron -
Sherman Oaks and Van Nuys are both communities within the City of Los Angeles (generally within LAPD Van Nuys Division).
NavigateLA Map Gallery will help with which LAPD Division (I would start with Van Nuys).
Sherman Oaks is indeed mostly in Van Nuys Division, however the LAPD maps in the NavigateLA site haven't been updated to account for the addition of Olympic and Topanga Divisions in January of 2009. The
west boundary of Van Nuys Division is now I-405 from Mulholland up to the Metrolink/UPRR tracks north of Sherman Way, with West Valley handling everything west of I-405.
Sherman Oaks is mostly in the patrol areas of Van Nuys units 9A63 and 9A89, but it goes a little west of I-405 into West Valley, to Firmament Avenue in unit 10A99's area. While they TRY to keep the "A" cars in their assigned "basic car" areas, a lot of the time that's more theoretical than real: for urgent and emergency calls, whoever is available gets sent to wherever they're needed.
It's not as fancy as NavigateLA's maps, but I have the current LAPD Division boundaries at
LAPD Patrol Area Maps. Sherman Oaks covers roughly the southern 1/3 of Van Nuys Division, and is bounded by West Valley to its west, West L.A. Division to the south, and North Hollywood Div to the east - all LAPD areas.