As / like

Hello teachers,

I have a question about the use of 'as' and 'like'. I thought 'like' was a preposition and 'as' was used before a subject + verb. However, I hear people say 'like' all the time. So what is the rule about it?

Are both the sentences below correct?

As I said yesterday, I'm thinking of going to Canada.
Like I said yesterday, I'm thinking of going to Canada.

I've just come back from my holidays but I feel tired and depressed.
I don't feel as if I've had a holiday.
I don't feel like I've had a holiday.

You look as if you haven't slept.
You look like you haven't slept.

Do you hear the music next door?
It sounds as if they are having a party.
It sounds like they are having a party.

After the interruption she carried on talking as if nothing had happened.
After the interruption she carried on talking like nothing had happened.

He walks as if he had a wooden leg.
He walks like he had a wooden leg.

He talks as if he knew everything.
He talks like he knew everything.

Thanks a lot.

Regards,
Henry