For the record, I'm taking this information from the most recent Ontario Residential Tenancies Act.
Yes, you can evicted from your home if you do not pay rent on the day it is due. However, you can only be evicted if the landlord gives you a Notice of Termination, and you can not be evicted until the 14th day after the notice is given (or only 7 days if you pay your rent on a daily or weekly basis). This notice must include the fact that the eviction can be avoided if you pay the amount due *before* the date it is to take effect.
So if your landlord gives you the Notice of Termination on November 1st, you can't be evicted until November 15th. If you pay your rent on November 14th, you can't be evicted anymore.
Right now, there are three organizations in Toronto you should call:
1. The Customer Service line for the Landlord and Tenant Board at 416-645-8080 (or outside of the 416 calling area, toll free at 1-888-332-3234). They will give you more information about your rights as a tenant and your landlord's rights. Explain to them that you paid first and last month's rent and ask them if that changes anything.
2. The Metro Tenant's Association hotline. They are geared to helping tenants, not landlords, figure out what their rights are and can also refer you to other organizations who can help you. Call them: 416-921-9494
2. If you receive a Notice of Termination, you should get legal help no matter what. You can find a community legal clinic which can help you; most have cheap or free services for people in financial need. Here is a list of community legal clinics in Toronto:
http://www.ontariotenants.ca/law/tenant.phtml#clinics
I hope this helps, and wish you & your family the best of luck!