The middle gear is a 24 tooth gear with integrated 2.5mm axle. The outer diameter is about 13mm.
The other two gears are a somewhat odd 9 tooth gear (Tomy used a lot of 8 tooth gears that were similar to this, but 9 is less common) and a partially-toothed cam to only activate the sound intermittently. It has five teeth covering a quarter of the gear - you best bet might be a 16-20 tooth gear that you remove some teeth from. It is a little hard to tell because there aren't teeth the whole way around but it looks like it would be about 8mm in diameter. These sit on a 25mm long 2mm thick axle.
The old mail car Annie is based on uses a grooved metal cam instead of a partial gear as well as a metal axle in the intermediate gear.
The TomyTrains chuffing car has a gear with two opposite quarters that are toothed but it is right on the drive axle. No nice picture of this one, its in storage right now.
I have a website where I have been writing about and photographing many of the sets and pieces that I find interesting.