You can take a train from Oslo to Åmål via Kil Station in around 4 h 16 min. Alternatively, Swebus operates a bus from Oslo to Åmål 4 times a day. Tickets cost $22 - $35 and the journey takes 2 h 20 min. FlixBus also services this route twice daily.
From Oslo S train to Kil Station then train to Aamaal Station. 4 h 16 min kr 412. From Oslo Bussterminal bus to Knöstad Bytespunkt, line 806 bus to Säffle station, then bus to Åmål station. 4 h 43 min kr 361. From Oslo drive to Åmål. 2 h 30 min kr 288.