I figure I have these options:
1. Find a job and get a work permit before my tourist visa expires in late June.
As mentioned, this might turn out to be harder than expected, and it is not something I can control.
My view FWIW.
Like you, I doubt you would have enough time.
2. Apply for an extension of my tourist visa
Do these usually get approved on the first time requests? When should I send in the application? If I send it right before my 6 months are up, can I stay in Canada while it is being processed? How long is it normal to ask for? Do you think it hurts to ask for a loooong time like 9 or 12 more months? I mean, can they say "You won't get the 12 months you asked for, but we'll give you 7 months", or is it more black and white where you either get the time you asked for or not? What does a stamp in your passport mean? Is it considered a tourist record? Can I go back to Norway right before my time is up, and then come back to Canada 4 weeks later and get another 6 months?
You can do this for $75
http://www.cic.gc.ca/english/visit/extend-stay.aspIt has to be at Vegreville at least 30 days before your visa (visitor record) expires.
What you ask for, and what you get are variable, some people get more time, some get less.
Once you have applied, you are on implied status until a decision is made (I believe leaving the country terminates the implied status).
I doubt that returning 4 weeks later would please them, but I cannot know that as fact.
3. Have my gf sponsor me as common-law
This would be great, but I am not sure what proof I need to present. We have lived together since August 2009, but have no shared bills or any other payments. I could write my landlord in Australia and ask her to testify that we lived together, but do not know if Customs would accept her word for it?
You could do, I expect it may need to be notarized. I would think you need more proof. You may get a better answer from someone else here.
You could get married and have your wife sponsor you
http://www.cic.gc.ca/english/information/applications/fc.asp4. Apply to become a live-in caregiver.
My uncle married a Canadian girl a long time ago, and they have two kids. We have not really talked about it, but they have said they would sponsor me. I do not however want to hassle them, and would prefer to get this sorted differently.
I have no idea on this, but it sounds like a last resort...
Other information: I have more than enough money to take of myself without working for the next 5 years; I have no crimial record or medical problems and as noted earlier I have a master degree. What is my best course of action here?
PS. When I picked up the unaccompanied baggage I got hassled by the IO, and she was asking me if I had reported this when at my point of entry, and I also got asked a bunch of questions when coming back from a visit to the Buffalo in the US. I am planning on going to Vegas in addition to visiting my girlfriend's family in Bermuda before my tourist visa expires. Does this seems like a bad idea? I'm just a bit nervous to get denied entry at the border as they always seem to be so suspicious of me, and I do not know what rights I have to leave and come back to Canada with just this stamp in my passport.
Once you are flagged you can expect a conversation at immigration, but now you have done it once the mystery is gone huh?

What does the visitor record say you can do?