Since you are a citizen, you can sponsor your wife while living in Canada or while living abroad. But as I understand, you'll only be visiting there for a short while, so you'll continue living in Canada. If you actually move there, then you'd need to supply evidence that you will move to Canada once your wife gets her visa.
As for a visa to Ethiopia... assuming you're not also a citizen of Ethiopia, according to this site (
http://www.ethioembassy.org.uk/consular/Visa.htm#How_to_Apply_for_a_Visa) you should be able to get the visa upon arriving at the airport.
Have you looked at the forms for sponsorship yet? Prepared the supporting evidence? And before you send in the application, your wife will need to do the medical exam and get all the required police certificates (for each country she's lived in for 6 months or more since turning 18). It's not exactly something most people put together in a week
No matter where you are when you send in the app, you have to send it to Mississauga. When they're done with their part, they will forward it to the appropriate visa office.
Assuming you're only sponsoring your wife, the fees for the application should be $1040. You can choose to pay $490 of that at a later point (this is the Right of Permanent Residence Fee, if you don't pay it now then the visa office will ask you to pay it when they're ready to issue a visa), but it's advisable to pay everything at the same time so that you avoid delays later on.
That doesn't include any fees you might have with the medical exam, police certificates, mailing the app and so on.
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