I think it can safely be said that every street in Toronto, no matter where it is located, starts near 0. Owing to lot and parcel severances, amalgamations, etc., some don’t necessarily start at 1, but it will always be a low number.
Streets that cross city/borough boundaries keep the numbering from where they began. For example, Lawrence Avenue East starts at Yonge Street in the old City of Toronto with 1, and its numbers grow as it passes into North York, and then into Scarborough. Numbering does not start from 1 again, just because the street crosses a municipal boundary. And as has been said, Lawrence’s numbers do not correspond with parallel streets: Eglinton, Sheppard, York Mills, etc.
To the best of my recollection, only when a street changes names does it restart numbering. A good example would be Duplex Avenue, which starts at Chaplin Crescent, just north of Davisville. Duplex runs north, as do its numbers; until it gets to Lawrence Avenue West. There, it continues north but is renamed Jedburgh Avenue, and the numbers start over at 1. Some blocks north of that, Jedburgh is renamed Ridley Boulevard, and the numbering starts over again at 1. It’s the same street throughout its distance, but when its name changes, so do its numbers.
It may be worth noting also that in Toronto, the words “street” and “avenue” (and for that matter, “road,” “drive,” “boulevard,” “crescent,” etc.) mean nothing–you cannot tell by such a word if the street runs north-south or east-west, as you can in places like Manhattan or Calgary. But what else can you expect from a city where a major thoroughfare is named “Avenue Road”? 