Pseudopods are only seen in unicellular protists. You see pseudopods are are actually temporary projections of the cell membrane. Worms move by contracting their bodies and pushing them forward, like a compression wave. Caterpillars have distinct feet and move them like a longitudinal wave.
Lamellipodes are also a strictly unicellular form of locomotion. Basically it's a sheet of actin underneath the cell allowing it to move around. Millipedes also have distinctive legs and move them in a wave like manner.
Snakes don't really move by flicking their tail. They wave their whole body to achieve this motion known as slithering, which should really be it's on category I think.
Yeah, while it's interesting to think about the great variety of forms of locomotion, we have to ask ourselves how we would implement them. It certainly wouldn't be one-to-one -- we won't have separate parts for slithering, etc.
Walking is (comparatively) easy -- you have a structure that will push you forward relative to the ground, which doesn't slide along the ground. That's 3 of your categories right there (and arguably a fourth, if you explain what you mean by jumping cephalopod tentacles).
All the aquatic ones will have to be handled in their own specific model -- body deformation producing thrust by imparting momentum on water (in macroscale) or by differential drag (in microscale). ORganic jets would be even simpler, as they are just sources of thrust without having to calculate effects of body deformation.
The land-friction ones, I am not sure how to handle. Earthworms and snakes move through continuous, cyclical motions, which in some ways work like microbes swimming (sliding means you generally act without inertia, for example), but in other ways not (loose solid particle flow is close to inviscid). I think it would be a model full of approximations, but I have hope that it will be good enough.
Jumping cephalopod tentacles is just my way of saying how they slowly contract and quickly expand to dispel water and therefore propel themselves. Plus, we can apply these techniques to vehicles, because, save for internal structure and maximum power, organic wheels work the same way as car wheels. Same for other parts. What I was thinking was how the OE concept had the ability to "tag" body parts as limbs and such. If you had a tail, you could set that to be a prehensile tail, slithering tail, et cetera. You would just need to adapt structures so it would be better as that function.