Hold on! At most airlines (AA is the one exception I know about), you can't upgrade at all (no matter how many miles you have) at UA from the lowest ("deep discount") fares. You first have to buy an upgradeable fare. (At some airlines, on some flights, the only upgradeable fares seem to be the ones just below "fully refundable"!)

At AA, you can upgrade from almost any economy fare (O or Q excepted in some circumstances, and btw those circumstances just decreased) by paying a co-pay (now $350 each way) in addition to 25000 miles. Depending on the airline, it may or may not work out roughly the same as other airlines which force you to buy a higher fare, with one key difference: The other airlines force you to buy a higher fare and then find out if you'll get upgraded or not, while AA only charges you the co-pay if your upgrade actually goes through.

Second, you cannot generally upgrade on partner or codeshare flights; it has to a flight operated by the airline you have miles with. So with all of these airlines, if you choose to stopover in Europe or the Middle East, you can only at best upgrade as far as the connection takes. While if you choose to connect in the US and fly a US airline that flies from the US straight to DEL, you at least qualify to upgrade all the way (if you buy a qualifying fare), though how realistic the chances of such upgrade are could be a separate question.

So you have to start by deciding, what is more important to you, the upgrade or the stopover (if you can only get an upgrade even halfway by choosing an ailrine that won't give you a stopover you value).

To your specifics, it's per journey direction (but only as far as the airline you hold miles with will take you, and only if there are upgrade seats available on all those legs). At any rate, you pay per journey direction (even if you succeed at upgrading only one leg). Most often, it's 25000 miles (plus co-pay at AA, or plus the increased cost on an upgradeable fare at most other airlines).