Bob, the shafts need to have good bushes/bearings because that is what holds them central, which is essential if you hope to make the oil seals work. There is a good chance the water entry happened because the input shaft oil seal couldn't cope with the loose (worn) bush. The bushes/bearings also control the proper center distance, and therefore meshing, of the worm and worm-wheel. So, you need to replace what is worn out.
I have no idea whether you can buy a gasket, but if you go to Repco or somewhere similar you should be able to choose a suitable gasket material, and cut your own.
The type of lubricant you use in gearboxes depends somewhat on the operating speed of the input shaft. If it runs at engine speed (3,000 rpm) that is out of the ideal speed range for grease, and requires oil. In general, thin (low viscosity) oils are only used when there are hydraulics involved, or an inherently weak mechanism. Many car gearboxes use SAE30 oil just because the synchronisers cannot handle the drag torque caused by heavier (SAE90 usually) oil. Other, better gearboxes use straight SAE90 oil. In this case, for a simple worm gear running at 3,000 rpm, SAE90 sounds about right. If it was only 1,000 rpm, you'd probably use SAE140.
The next issue is to inspect carefully for any copper/brass/bronze parts in the gearbox, or any sealed bearings. These items cannot stand hypoid gear oil (commonly called Extreme Pressure, or EP). EP oils have substantial amounts of sulphur added to them, to act as an anti-seize compound between sliding metal parts. You can recognise the sharp, unpleasant smell of oils containing sulphur. If you have no copper-based alloys or rubber parts, you might as well use ordinary EP90 automotive rear axle oil: it won't do any measurable harm, it's much easier to get, and it helps keep the worm from seizing onto the wormwheel (there are high sliding velocities involved, and sometimes extreme conditions when something digs into a water pipe and tries to lock up the tiller).
Having said all that, why not ask the manufacturer what lubricant to use? That is the safest, and usually the easiest, way.
