Any type of refua is ossur on Shabbos. Chazal were concerned lest it lead to grinding medicinal herbs which is Tochayn. (MB 1)
If oil is used to anoint healthy people, it may also be used as a remedy for a sore stomach or for skin ailments. The reason is that such anointing is not viewed as Refua since maybe he’s anointing because people always anoint even when healthy. (ShA 1 – MB 2)
If a certain oil is used only for refua, it’s ossur to use on Shabbos. In fact, in places that no-one anoints except for refua, all oils are ossur. (ShA 1 – Rama 1)
You are allowed to give a light massage on Shabbos for pleasure's sake. You can even apply oil with a shinui – add the oil at the same time of the rubbing. (ShA 2)
A rigorous massage with the intention of making the patient sweat is forbidden. (MB 7)
Do not use a back scratcher on Shabbos – it’s uvdin d’chol. Although, if there is dirt on your skin, you are allowed to scratch it clean with a backscratcher. (ShA 3 – MB 8)
You may use a special backscratcher designated for Shabbos. This is similar to what the girls use for flattening (not combing) their hair – a designated Shabbos hair brush. (MB 10)
Scratching with your fingernails is mutar, just don't make yourself bleed. (MB 9)
Polishing shoes with wax is the melacha of M’marayach. If a non-Jew does it for you on Shabbos, you may not wear the shoes until after Shabbos plus the time it took to polish the shoes., (MB 16 – ShaH 17)