Transformer that age and size I would put at around 80-100VA, and from the construction I would guess it was to power some valve equipment, so will have a primary with 2 coils of 0V, 90V, 100V, 105V, 110V, 115V and120V, which are either run in series or parallel to allow it to operate from 90, 100, 105, 110, 115, 120, 180, 190, 200, 205, 210, 220, 230, or 240VAC mains ( valves needing a tightly regulated heater voltage and anode voltage), with likely secondaries being a 6.3VAC 5A winding, a 300, 0,300VAC winding, a heater winding of 6.3VAC for the HT side ( insulated to 600VAC for safety) and possibly a 75-100VAC winding for bias supplies.
At the probable age, and seeing as the insulation is paper only, using it would be hazardous. I would suggest taking it apart to see how it is made, and the insulation used. Then at the end you will have 1kg of scrap copper and about 2kg of scrap iron. Inside you will probably find purple insulated wire and other colours, which are not common these days, as the insulating varnish then came in a few colours,, while modern ones are mostly light yellow or clear.
As to stuff in water and rain, you might find they will work once dried and after cleaning ( water wash for mud, oil and such you might want to use soap first then rinse with water) and then test and use those without bad corrosion. However anything with paper insulation ( capacitors with paper coverings, transformers and such) might take months to dry out, even if kept at elevated temperature like in a warming drawer for weeks. Electrolytic capacitors that have sat in oil will likely have the rubber bung gone soft, so if it is soft scrap it, otherwise use it. It will have limited life left in any case.