Should I put straw and stable manure around or all over the strawberry plants?
Around would be best. It will rot/weather down over the winter months.
I would not put it on the strawberry bed at this time, would stack it close to them and spend some time clearing any weeds , dead foliage, stray runners and old straw to the compost heap,thereby removing problems for next season. It is not good to provide nitrogen to them at this time of year ,it will encourage soft growth only to be cut back by frosts ,hopefully anticipated in the next few weeks.
The 'better rotted by February' material can then be applied at the first signs of regrowth, having again removed old foliage.