Have got the manual of Corolla & gone through the Oils page.
Here are the details what Toyota recommends in their manual issued by Indus Motor Company Limited.
2NZ-FE 3.7L (with Filter)
1ZR-FE 4.2L (with Filter)
2C 5.1L (with Filter)
Oil Grade: 5W-30 and 10W-30
API Grade: SL, SM
Can also use 15W-40 and 20W-50, SL or SM grade.
(Page no. 280, Lubrication System)
For Diesel Engine: G-DLD-1, API CF-4, CF, 5W-30 and 10W-30 (Page 282)
COOLING SYSTEM CAPACITIES
Coolant type: Use either of the following
> Toyota Super Long Life Coolant.
> Similar high-quality ethylene glycol-based non-silicate, non-amine, non-nitrite and non-borate coolant with long-life hybrid organic acid technology.
Note: DO NOT USE PLAIN WATER ALONE.
GEAR OILS FOR MANUAL TRANSAXLE
2NZ-FE 1.9L SAE 75W-90 API GL-4 or GL-5
1ZR-FE 2.4L SAE 75W Toyota's Gear Oil LV or equivalent. API Grade is only GL-4
2C 2.5L SAE 75W-90 API GL-4 or GL-5
GEAR OIL FOR AUTOMATIC TRANSAXLE
Fluid Capacity 6.4L
Fluid type Toyota ATF WS
MY TECHNICAL SUGGESTION FOR CHOICE OF ENGINE OIL (its not in the manual though. lol)
Please DO NOT be panic to find only the SL or SM grade engine oils because manual says so. Plz don't. Instead, try to choose SN Grade oils (which is latest standard) and more importantly already covers all the characteristics & properties of previous grades.
Example: SM grade oil surely has the properties of SL, SG, SH, SJ, grades (the older ones, but it will not meet SN standards). Hence if you will choose SN, then it will automatically be having properties/characteristics of SM, SL, SG, SH grades plus the new ones which makes is SN.