Normally stripping is done to remove any detergent build-up that has occured (that can often cause unpleasant odors) so for that situation one wouldn't use detergent to start with. I'm recomending that for you because you're not trying to remove detergent build-up but a possible fabric softener build-up. Fabric softener is a waxy type build-up so it's easiest to dissolve this with both detergent and hot water. I wouldn't worry about buying a special detergent just to do this, but if you already have one that's a little stronger then you could use that one (say as opposed to a really gentle environmentally safe detergent). You could use a squirt of dish detergent if you wanted to, or Sunlight, whatever you have handy...
Honestly though, I would wait and see once you get the diapers. There might be no build-up at all, or only a mild harmless build-up that would go away after a few regular washings.
You can buy tea tree oil at pretty much any pharmacy, it's actually more common than one might think. It's fairly expensive at $10-$15 for a small bottle, but since you litterally use it drop by drop it goes a long long way. Vinegar is a useful laundry additive and used full strenght it does disinfect well, but diluted in a washer full of water it loses it's disinfecting qualities. So while it can be useful in stripping (the acidity helps dissolve detergent build-up and can help rinse detergent out in your every day diaper washings) I don't think it's a very good substitute for tea tree oil unless you plan on soaking your diapers in pure vinegar. You could do that but I don't think it's worth the trouble personally...
As for regular strippings, everyone has their own particular way of doing things. Some use dawn at the beginning, some use a heavy vinegar soak to start things off (like 5-6 cups or more in the washer to help dissolve build-up), some use Oxy-Clean (or any generic oxygen bleach), some use baking soda, or just a small amount of vinegar, some up the temperature on their hot water heater temporarily, some use the 'sanitize' cycle if they have one etc etc... The basics is just to put the diapers through one or more hot water cycles. Any additional steps are up to you...
Other than stripping used diapers I wouldn't worry about ever having to do it afterwards. As long as you don't use too much detergent on an everyday basis (like no more than 1/3-1/2 of the 'recomended' amount at the very very most), you shouldn't have to ever strip your diapers. Some do find it helpful to do a small stripping on a regular basis like once a month, but I'd wait and see if it's really necessary. Most people never have to do anything other than just regular washings to their diapers...
Karen.