So which should go on first, the Walnut oil or the sanding sealer?

Oils penetrate into the wood pores
Sealers clog up the pores, sealing them from further penetration

If you put the sealer on first, the oil will not penetrate

Where and how it's going to be used usually determines the finish.

Don R Davis wrote on Nov 3^rd, 2019 at 9:22pm:

if, as I'm guessing, your sanding sealer is shellac, you need to be careful.

Padauk
Here is some info that I cut from various sources. They all have the same conclusions and I don't have to write it all down. 

Because padauk’s pigment is alcohol-soluble, brushing or wiping on shellac can cause the color to bleed or smear onto adjacent lighter woods. To avoid problems, spray on a few light coats of shellac to seal the color before using a brush or rag to apply subsequent shellac coats. Alternatively, use lacquer or varnish.

The wood’s natural oils have been known to retard the drying times of oil-based varnishes, but don’t seem to affect water-based finishes. (Wiping the wood with acetone can help by removing some of the surface oils, but test the wood before you commit to a particular finish.) Oil-based penetrating oils or wiping varnishes are generally a good choice, although they tend to darken the wood more than water-based finishes.
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Almost every forum having anything to do with woodworking has at least one thread devoted to finishing padauk.

Seems counterintuitive to apply a penetrating oil finish on a sealer surface.  But if you are comfortable with it and like the result keep doing so.

Your experience with a wiping oil is quite normal- I sometimes have to apply 3 coats of wiping varnish  before the wood stops showing dry spots.  And that is a shop mixed wiping varnish with probably more resin than commercial ones.