"a strange-noise-making machine" correct
"a make-strange-noise machine" incorrect
I would understand a strange-noise-making machine to be a machine whose purpose is to make strange noises, just an ice-cream-making machine is a machine whose purpose is to make ice cream.
However, it could also mean a noise-making machine that is strange. So it's kind of ambiguous, but it's not too bad because we can work out the meaning from the context.
You could also say it like this:
"a machine for making strange noises" That is, a machine whose purpose is to make strange noises.
"a machine that makes strange noises" That is, a machine (of unspecified purpose) that makes strange noises.
I take it that you are making a joke something like this:
"What's your motorbike like?"
"Oh, it's so worn out, it's more of a strange-noise-making machine than a motorbike at this stage." Or, "That's not a motorbike. That's a strange-noise-making machine."
I think those would be fine.