I believe the avoid side slipping on a 172 comes from the older models with a 40 degree flap setting the newer models now have a 30 limit. Same with 150 40 max 152 30 max. The warning on some models which is not mentioned in the POH is don't open the throttle in the slip, always go back to balanced flight as some model will roll on their backs so fast you won't catch it. Happened to a site seeing C177 crossed controls for a good view pilot opened her up and she rolled in. On the 177 flap limit is 30 so it can be side slipped with them down.
Shut down as per the POH but I believe slipping away from the flames can be a good Idea fire walls don't hold up for ever.
In an oil fire if the engine can be stopped may be a good idea so on a VP pull to course pitch and slow down to stop the prop will reduce drag as well a bit more glide distance.
When I had an engine failure with oil smoke coming from the cowl no time as to low flight only lasted another 60 seconds.