Oberoi is situated next to a green zone (Aarey colony). It is also next to the highway. Transport can be horrible though, as the roads are packed, especially at peak times. If you are planning to enjoy the expat events in the south of Mumbai (as there are many), you are long drives away (from anything in between 1 and 3 hours). On the other hand, it's more green here, and easier to leave town to the north (there are some get-away places). For those trips, it's best to hire a driver.
Yes, Mumbai is not an easy place to live. No big shops, all is rather shabby, and you will be in rikshaws a lot (they do have meters, so no bargaining necessary). If you live next to the school (in Oberoi Woods), you have a great advantage: you can walk to school. Many of the staff with kids live here. There is a play area (nothing special) and a pool. Kids can run around safely.
The Oberoi mall is close by, you can even walk there. Cinema, some restaurants and the obvious brand shops. Imported wine and beer are expensive, but local wines form the Nasik area are alright to enjoy.
You can/will have a maid/nanny, affordable. Health care is good in Mumbai. You have a high deductible though (Scholar/Clements). Buying meat is not as easy as back home, specialised shops or a few of the big supermarkets carry supply. Many Indians order (just about anything) on-line. Works great, and you save time.

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Students: for the majority -> lovely and mostly Indian. You will like them.

Hope it helps a bit