Swedish politician: "Ladies and gentlemen, I welcome to this technical mess."
Answer
NO/DK messe SE mässa = 'trade fair', cognate with EN mass in the Christian sense
Norwegian at an international conference: "I am sorry, this microphone smells each time I speak."
Answer
NO smelle SE smälla = 'to make a loud noise, to bang or slam etc'
Ole Einar Bjørndalen: "Maybe we can invite him over to our hotel, we have a really good cock with us."
Answer
NO kokk DE kok SE kock = 'cook', cognate with EN cook via PWG *kok
These next few all come from our beloved Petter Solberg:
"It's not the fart that kills you, it's the smell."
Answer
NO/DK/SE fart = 'speed', NO smell SE smäll = 'bang'
"I had bad pigs in my deck."
Answer
NO/SE pigg DK pig = 'spike, barb, quill, prickle' NO dekk DK dæk SE däck = 'tyre', cognate with EN deck via Middle Dutch dec ※NO piggdekk refers to studded tyres
"It was a moose in the engine."
Answer
NO/DK/SE mus = 'mouse', cognate with EN mouse via PGmc *mūs whereas EN moose derives from Proto-Algonquian *mo·swa, lit. "it strips [i.e. the bark off trees]"
"It was so much dog on the window."
Answer
NO dogg or dugg DK dug SE dagg = 'dew', cognate with EN dew via PGmc *dawwą
"The rat is loose! The rat is loose!"
Answer
NO/SE ratt DK rat = 'steering wheel', ultimately related to English words like rotor via PIE *Hreth₂- 'to run'
The moose and cock ones I have heard before.
I'm surprised it's those you've heard before, "it's not the fart" is in my experience by far the most famous of these quotes.