I edited my response, as I realised there are different meanings depending on the preposition.
"Jeg søker etter en job" = "I'm looking for a job".
It would probably be more common to say "Jeg leter etter en jobb" or "Jeg prøver å finne en jobb" (last one: I'm trying to find a job)
Was about to inquire about that. I'd heard søker etter in one of the verb lists on the old tree, but don't remember seeing søker på. Takk for forklaring!
Question: Can you use søker på for when something applies, for example Verktøyet søker ikke på - when something doesn't apply to a situation?
Searching/looking/seeking all mean roughly the same thing - you're browsing through job sites, perhaps registering with recruitment agencies. Seeking/searching arguably have a bit more urgency and direction about them - you're not just seeing what's out there, you're actively wanting work - but that's not going to be true in every region English is spoken.
Applying, on the other hand, means that you're actually sending your CV/resumé/application form to employers.