"Muntre opp" means "cheer up".

"Oppmuntre" can mean the same, but also includes most of the English uses of "encourage". This is the most direct translation.

"Oppfordre" is closer to "advise". "Jeg oppfordrer alle til å vaksinere seg" means "I advise everyone to get vaccinated". "Oppmuntre" is using emotions, "oppfordre" is more logic based.

Avslå = decline. Nekte = refuse.

"Veldig" is the most common translation of "very". "Svært" not so much. You can easily go without using it at all, at least in the meaning of "very".

"Trenge" and "behøve" can pretty much be used interchangeably. "Trenge" is slightly more versatile, and just as with "svært", "behøve" can always be exchanged with "trenge". Their use vary between dialects.