If you want an oval cross section, build yourself (or buy of course) a traditional pole lathe.
Everything that is or ever was, made on a pole lathe is slightly oval in cross section by default.
That's one of the ways you can tell genuine, original
old Windsor chairs, from mass produced versions, just check to see if the spindles are round or oval, if their oval, their almost certainly
very old or else hand crafted by a more modern bodger. Same goes for staircase spindles and chair legs etc. It's something to do with the fact that the job rotates both forwards
and backwards and you only actually cut the wood with the chisel/gouge etc when its turning on the down stroke ( top towards you).
As for the actual finished shape, you can have as simple or intricate as your skills and tools allow.
I'm not sure how you would bore the centre holes mind you
I made a few bark awls a few years back, with handles I'd turned on my pole lathe and every single one was slightly oval in cross section, as were the fishing priest blanks, bog pull handles and other odds and ends. I've not made anything on my pole lathe for about 8 years now, since the pole lathe stepped in to serve as a trestle for my canoes! It's free again now though. I should really get it spinning again but I've little or no raw material and even less interest if I'm honest.
I was actually thinking of selling it but you tend to need a shave horse to go with the lathe and it'd be a strictly collect only job!