I have a couple of live edge slabs I was planning on making into live edge end tables but I'm wondering what to do with the cracks in the side - if anything can be done at all. Could I fill them with a glue/sawdust mixture? Would some other commercial product be better? Is it worth attempting at all?
Could I fill them with a glue/sawdust mixture?
You can yes but common woodworking glue (PVA-type, white or yellow) wouldn't necessarily be the best choice for the glue.
A much more solid fill can be made by using epoxy. Filled (or just coloured) epoxy is now a common material for filling voids and defects in wood. To a degree this kind of filler can stabilise a crack and add strength, but without some further means to hold the wood steady (e.g. a butterfly key, hidden bolt or dowelling) a crack may continue to open up, so it is worth taking at least one extra step as a safety measure.
Seconding the suggestion to use epoxy. That crack is an interesting one though because it goes through the nonflat surface of the live edge, so its a bit challenging to make a mould to stop the epoxy from leaking out.
My suggestion would be to build a mould that holds the slab on its side (with the live edge on the top), and pour the epoxy in from the live edge. I did a live edge slab project recently and built a somewhat similar jig for that purpose. In your case since the gaps are bigger I think it would be worth using a proper melamine mould (with vices holding it into the slab) to seal the crack on the flat faces.