You will need to ask EVA to check your bags through to your final destination. If you are on two itineraries, they may or may not agree, it depends on the agent - I had no problem having Air Canada at NRT check my bags through to United at YVR and I did not have to claim the bags. If they agree, then you do not need to reclaim the bags in YYZ, they will be transferred to UA, which is the normal practice, but since you are overnighting, I cannot guarantee that your bags will be held in the transit area because technically they are passed through the Customs inspection process in real time as you transfer. Also, while your bags are sitting overnight in the transfer area, you are giving the not-so-bright Swissport nitwits ample opportunity to go through your bags and help themselves to your personal contents. So, because you need to exit the airport anyway, as mentioned above, I would just check the bags through to YYZ, and thus here is your work plan:

1. you must be admissible into Canada, and if you are not using a US passport, you may need a ETA or a visa. Taiwan nationals who are not a US permanent resident will need an ETA to fly to or through Canada.
2. *if* you decide to have your bags checked through to your connecting flight, then after entering Canada, while still in baggage claim, go to the EVA baggage office and ask them to check where your bags are - they will call down to their ramp staff and let you know if the bags were handed over to United for the night, or are being sent up to baggage claim for you. If the former, just leave the airport, and if the latter, wait for your bags and then leave the airport with them.
3. you are on your own, so I would book a hotel near the airport - if your connecting flight is in the morning, and you are not a Nexus or Global Entry member, it can take 90-120 minutes or more to clear security and US pre-clearance, so make sure you are at the airport early enough. I've seen wait times approaching 3 hours, especially on Monday mornings.
4. if your bags were transferred during the night, just use a United kiosk in the morning to check-in and get a boarding pass, otherwise you need to budget another 30 minutes to get through the check-in line to drop your bags at the United counter
5. when going through US pre-clearance, they will have access to your checked bag as needed, then it will be handed off behind the scenes to United for boarding on your flight
6. when going through US pre-clearance, both you and your baggage contents need to be admissible to the USA - so be aware of what is inside - and this is another reason I would suggest not checking the bags through and leaving them in the transfer area overnight, given those Swissport dimwits might decide to ADD something to your bags for retrieval at your final destination, that could cause you trouble if discovered by US Customs