Re: English playgroups in Oerlikon?
Have you checked out the TEZET Quartierzentrum in Oerlikon? It's on Gubelstrasse. They have two English speaking playgroups - one on Wednesday afternoons and one on Friday mornings both are held on the second floor.
The TEZET also has a great (and free!!!) indoor playroom on the ground floor (called the Innenspielplatz) which is open Tues to Fridays, 10am til 5pm. There's a playhouse, an indoor slide, a climbing frame, a small trampoline, some ride-on cars and various other toys. A very useful place for a change of scene or when the weather is bad - your kids can burn off their excess energy running around. As a side note, I've met loads of English speaking mums at the TEZET. There's a nice little cafe there too.
If you are looking for an English speaking pre-school type of place, there is the Happy Nest in Oerlikon which I can recommend highly, but I believe your child needs to be 2.5 to join.
Hope you find something!