Sealing gap between foundation and external wall
It looks like your siding is wood (probably cedar). You don't want to seal this too much - the underside of these shakes/shingles needs to be able to release moisture or your siding may rot sooner. Best option is to seal from the inside, probably with spray foam.

Edit based on comments: because you've indicated this is an inaccessible crawlspace, you should consider two other measures:


Apply pesticides around your foundation, under the edge of the shingles, and at crawlspace vents. These can help control the vermin problem without perfect sealing. (Powder treatments including diatomaceous earth are pretty effective and easy to use for ants and similar critters, but you'll want to target whatever particular vermin you've seen.)
Get access into your crawlspace and inspect there. If the crawlspace has no floor and vermin are digging through the dirt to get inside, extra sealing at this seam would have no effect. However, better sealing from inside the crawlspace could seal your walls and floors for better insulation and critter-resistance. Adding a moisture/bug barrier on the floor may also help. And you may find a bigger issue, like a colony of ants/termites/whatever established in your crawlspace.


I'd encourage you to get access into your crawlspace and inspect there -- it's really the best way to ascertain the cause of your critter problems and enables the most effective solutions.