Being a north Indian, the only onions that I have used and seen others using are red onions. These are used in all Indian traditional dishes.  I have seen green onions and white onions in the market sometimes (haven't noticed anyone purchasing them though).  How are the green and white ones different from the red onions I'm used to? Are there specific times I should use them instead of red onions, or things I should try them in to be able to tell the difference? 
The difference for green onions will be most noticable if you don't cook them.  Instead, slice them up and use them for a garnish over the dish.  The white portion of the green onion will still be oniony, but not quite as strong as a raw red onion.  Slice them thinly and use for garnish if you really want to bring out the onion qualities of them.  If you don't want it too strong, then add them when you're cooking.  (and you might not want to slice them as thin).  The green portion gives a more mild onion taste but also some of the grassy quality that you might get from chives.  I treat them like a fresh herb, chop them up, and add in them in the last minute of cooking or I don't cook them at all.  As for substitution ... I'd only plan to do it if you were cooking for someone who didn't like onions, as they're milder and come in smaller portions than bulb onions, so it's easier to control amounts without any waste.  ... and I'd do it if I had them on hand but didn't have bulb onions around.  If you're just looking for a good way to feature the green onions -- grill them.  Trim the ends off, clean off any dirt, give them a coat of oil, then toss them on a hot pan or grill.  They make a great side dish.  Other good uses are to add them into scrambled eggs, green onion pancakes, or press them into naan before cooking it.  ...  For the white onions, the opposite is true -- they're generally stronger than red onions.  Most people don't serve it as a raw garnish unless it's very thinly sliced and used in small amounts.  It's still used raw, but it tends to be blended into other things such as pico de gallo, or guacamole, where the pungency of the onion helps to balance out the sweetness of the tomatoes or richness of the avocado.  I'm having difficulty thinking of a dish where the qualities of the white onion would stand out, though.  My only idea is french onion soup, because it just comes out lacking if you make it with sweeter red or yellow onions ... but unless you made them side by side and compared them, I don't know that you'd see the difference.  You might try cooking them slowly over medium heat until they caramelize ... it'd let you feature the onions without them being overwhelming, and it brings out some of their more interesting qualities. 