Hello, what a lovely city, I have been there!
You undoubtedly already know the most obvious...papaya grow fast, fruit young, they aren't very pretty, but the leaves and flowers are edible, too...
Bananas of course
Star fruit, I think, can fruit while the tree is still young...
Lime trees have very fragrant blossoms...they do well in pots...
I don't know about strawberries, I think the humidity and lack of seasonal change might do them in, they would do better in India at higher altitude, I think...
I wonder, though, if a kiwi might do all right...going to check...

Oops...they grow up to 20 feet so you would need to train them on an arbor...
http://www.gardeningknowhow.com/edible/fruits/kiwi/growing-hardy-kiwi-vine.htm

Sorry I forgot to mention. I have two papaya trees, a flowering creeper and an Indian flowering tree called "nithyamalli" and "kozhukataimandarai" resp. Sorry i don't know what they're known as in English. :D . I also grow Aloe vera, Betel leaf and some Spinach on the terrace. :)

I thought nithya malli was a jasmine?