There is already a question about Shaving / Haircut / Nailcut - what days are allowed / prohibited?. So, I want to know the days I can take an oil massage (otherwise called as Abhyangana snana) including weekdays as well as the days as per the lunar calendar followed by us.
You are basically asking about Abhyanga Snana (oil massage followed by bath). And scriptures definitely talk about that..
The book Dharma Bindu (hosted by the Kamakoti.org) has the details:
Bharadwaaja Maharshi details these snanas as follows: Abhyanga snaapane yogyaa vaaraaye tithibhissaha,
Kathyate tethunaa spashtam pushtaye balavriddhaye/
Indorbudhasya sourescha vaarebhyangam prashasyate kaantim,
Shriyam tathaa dadyuh bhogaan vaaraadhipaah kramaat/
Dwiteeyaadyaashchatasrascha prashastaah Saptami tathaa,
Navami Dashami chaiva Trayodashyapi cha smritaah/
Bhaanu bhoumaamaraachaarya Shukravaareshu sankrame,
Vyatipaatecha Janmakshenaabhyangam snaanamaacharet/
Ekadashyaam charurdashyaam Ashtamyaam pratipadyapi,
Shashtyaam Parvaani chaabhyanga snaanamnaiva samaacharet/
Uttaraa phalguni jyeshthaa Shavanaardraasu raatrishu,
Abhyanga snaapanam dheemaan sukhardhi varjayettathaa/
Shishurogaarta vriddhaanaam yathaakaalam shareerinaam,
Abhyangoshnodaka snaanam naiva doshaavaham smritam/
Abhyangana Snaanas prescribed for health and strength are prescribed as follows: Monday, Wednesday and Sunday are excellent for these as they grant brightness, opulence and enjoyment respectively. Tithiwise, Dvitteya-Triteeya-Chaturthi-Panchami, Saptami, Navami and Trayodashi are auspicious. But, Sunday-Tuesday-Thursday- Friday Samkramana timings, Janma Nakshatras, Vyatipata timings are avoidable. Also, Ekadashi, Chaturdashi,Ashtami,Prathama,Shashti and Pournamai are unworthy. Uttara Phalguni, Jyeshtha, Shravana, Ardra nakshatras are to be avoided. Children, persons suffering from diseases and old aged are exempt from the above restrictions and might bathe with hot water.
This above list has the details of the prescribed days based on Vara, Tithi etc.