Awwwwwwwwww what a cutie! Has he got a name yet? Thank you for rescuing the little guy, crows sure can be merciless to babies fallen from the nest! Are you sure the crows were responsible for removing his wing and tail feathers though? Not wanting to scare you, but he could be a "runner", which is the name given to young lorikeets who might have psittacine beak and feather disease (PBFD), and it's the reason why some babies have no wing or tail feathers. It's fairly common in babies here in Queensland but not so sure about where you are, though you can have him tested for it by an avian vet. It is dangerous and pretty contagious so you would be wise to make an enquiry with a vet, particularly if you have friends who have birds because you would want to keep them safe from it.
What are you feeding him? I feed my varied lorikeet Wombaroo nectar for his wet mix at breakfast time, and he gets a combo of Passwell's and Attraction dry powder which I leave available for him all day. Wet mix should be discarded after about 3 or 4 hours as it will spoil after that time. Apologies if you know this already, but you haven't mentioned what you're feeding. You can feed fruits like apple and pear, and green leafy veg too. My guy is heavier on the veg than fruit cos he just doesn't need the extra sugar since he doesn't burn as much energy as the wild ones do. He LOVES things like broccolini, celery and bok choy. Things like citrus fruit and kale should be avoided as they can contribute to iron storage disease, something that lorikeets can become quite susceptible to.
Poop comes with the territory with lorikeets!! Don't be tempted to feed him pellets that are supposedly made for them. They are made more for the convenience of people, and all they will do is make him feel constipated. Lorikeets are evolved to eat nectar, flowers and fruit in the main, so we should not go against all those millions of years of evolution as it is to their detriment. My guy has actually potty trained himself pretty well and rarely has an accident on me, which is GREAT cos I wouldn't even know where to start trying to train him myself!
I'll leave it up to others to advise you with recall training, or indeed any other type of training, as it's never been my forte - my lories have always walked all over me! Do be aware though that rainbows can get pretty aggressive and bitey once they reach sexual maturity. Again, not trying to scare you, but it's something to be aware of. The following resource may help give you more insight - it's an older website but the info is still pretty good ...
The Lory-Link is here to help people source contacts with other Lorikeet owners in New Zealand and to be able to get help or advice on problems. This is also a great way to swap ideas, locate birds and learn more about keeping lorikeets in general.
www.kcbbs.gen.nz
In all honesty, I think your next best step is to have him wellness tested by an avian vet if you haven't already done so, just to rule out anything nasty, whether it's PBFD or something else. Plus avian vets are an absolute gold mine of info in terms of things like behaviours and training too.
Welcome to the wonderful world of lorikeet craziness, and I wish you the very best of luck!!!