We just did this with our youngest with both the bottle AND the nuk (he's now 21 mos old). Be direct and FIRM. I just told him, nope, no more bottles, you're a big boy now, would you like a cuppy of milk instead??? Make that part REALLY EXCITING and upbeat. If and when he throws a fit, make sure he can't slam into anything and walk away. When he's calmed down, offer the cuppy again...or another diversion. It sucks, but it'll be OK! I PROMISE! I don't recommend the soft NUBY cups, I know someone whose 4 year old STILL INSISTS ON ONE AT BEDTIME. One habit for another, I suppose. Works the same with potty training, too. Go right for the undies. But that's a whole 'nother topic!! Be firm, be supportive and he'll get it. A little extra snuggling, reading, rocking, etc during the roughest times (naps and bedtime) helps too. Just don't let him take advantage...they learn that too fast! :)
Good luck, I feel your pain!
C.