I am travelling from Winnipeg to Auckland with an international connection at Chicago (2hr 20min). I am a Canadian citizen and will go through pre-clearance check at Winnipeg but would I still need to claim my baggage and drop it off again at Chicago or not? Also 2hr 20 min. of connection time is enough to change terminal from 1 to 5 as only bus shuttles are operating at the moment. I am travelling via United and Air New Zealand. Any information is much appreciated. Thank you.
You'll be fine going there. As you note, you'll pre-clear US Customs in Winnipeg, and barring exceptional circumstances (which I've never had to deal with in my 30+ years of flying back & forth across the US border) you won't interact with US Customs & Immigration agents in the Chicago airport at all. Effectively, your YWG–ORD flight will be treated the same as any other flight arriving to ORD from a destination in the USA. You'll clear New Zealand Customs upon arrival in Auckland, and your baggage will in all likelihood be checked through to AKL in YWG (though you may wish to confirm this with the gate agents in Winnipeg just for your peace of mind.) All you'll have to do in Chicago is get from one gate to the other, and 2h20m is ample time to do so, even given the terminal change.
Note, however, that returning will be different. Assuming you are flying through Chicago (or another US destination), you will need to re-claim your luggage, pass through US customs, and re-check your luggage there. Along with the time required to change terminals, this will be a more time-consuming procedure.