Ok, the recipe seemed strange on first sight but it turned out great with some changes. I used buttercup squash (not butternut), 3 XL eggs, and I added some nutmeg, milk, and vanilla extract. The cake batter was becoming very dense while I was mixing it and I realized that the initial "problem" was the lack of milk. So I added about 1/2c milk to lighten the batter and I didn't add all the flour mixture. The cake came out really well, perfectly sweet, and not very dense but spongy in texture. Next time, I'll reduce the oil to 3/4-1c and sub the remainder amount with milk.
So moist and delicious, this is excellent cake! And it is very nice topped with a little cream cheese frosting.