How are you doing?
As you mention, WD-40 can be a help if there are lots of stubborn hardened grease, but for lubrication you need a better oil. You can get far with basic sewing machine oil, my favorite is Finish Line Ceramic Wet lube (gold cap), it is light, dissolves old grime and dirt very well, and make parts runs a notch smoother than most oils. Another favorite for vintage machines is Tri-Flow, both the oil and the grease. There are lots out there but generally these are the only ones I can safely recommend. They will work ideallly in the long run. This model takes grease on the open gears.
Several of the light spray can oils can help to speed up the initial clean up process, but be extra careful to wipe off and apply a good oil frequently, even daily oiling and test sewing for a period. The 401 will respond to thorough cleaning and repeated oil applications, test sewing, moving levers and knobs, etc. With this model it takes a bit of effort to make new oil seep to the inners of joints, gears and hinges. As oil oil start to dissolve, it takes repeated oiling and wiping off excess to flush out all sticky grime.
You machine looks a bit dirty, tan machines often do. Old oil mess cause staining like that. On the pluss side, it looks it is in very good condition under there.
This is one of the best tutorials on the 401, and there are a couple of very good threads on this forum too.