Interesting job you had there. Did you take any 'In Progress' pictures for us? I'd be interested in seeing how you made them.
Another use I remember for Elm was the making of coffins, as it resist rotting in 'damp' environments.
To throw my 2 pence worth in to answer your questions, All wood swells when it absorbs moisture so yes it will tighten on the shaft but by how much I don't know - I've seen an article on wood absorption etc if I can find it I'll post it.
By oil I presume you are talking about motor (mineral) type oils not our highly refined Danish Oils full of drying agents etc.
Again any moisture that enters the wood will cause swelling, but if it was oil I would assume that yes it would repel water/moisture to quite a high degree and also provide a lower friction, load bearing surface if the wood swells just that little too much. For Wagon Wheels I think Tallow (animal fat) was used.