Is it correct to say "jag var fyra år gammal då jag åkte till Norge" and if so, does it mean the same thing?
Yes, it means the same but it's more formal.
Det är en bra sak när pratar du formellt och vet inte om det :) Men, om du säger formella fraser i svenska, låter du korrekt, normallt? Tack!
Det låter lite onaturligt så jag skulle inte rekommendera det. Det passar bättre i skriven text än i tal.
Does it mean the same thing if you remove the word gammal?
How do you pronounce "var?"
The pronounciation looks pretty straightforward to me. Here is the answer to all your questions : forvo.com
Like "vawr" with the "aw" sounding like the "au" in "Australia"
Isn't it correct to say 'when I came to Norway' instead of 'went'?
Surely it depends on where you are now? If you're now in Norway, you'd say "came", but if you're now in some other country, you'd say "went". At least in English.
It's correct, but it would be när jag kom till Norge in Swedish instead.
Is it implied that the person talking moved to Norway? Or was it just a holiday?
No, not moving. Had they moved, it would have been "när jag flyttade till Norge.
You left out the word old!
When I try and pronounce this at more then a snail pace, my brain begins to overheat.
Well listening to this sentence makes me feel over my head.
In Swedish do you need the word "år", or can you just say "4" as in "Jag var fyra när jag åkte till Norge"?
"I was 4 when I went to Norway" is fine in English.
Travel agency Barnevernet.
'I was 4' should be accepted. We don't usually say 'years old' in English