Providence to Stoughton's easy. MBTA commuter rail from Providence goes right through it. NOW, Stoughton station to Ikea's the hard part. I don't believe there are any buses and it's a few miles (practically in Brockton). You'll probably need a cab for that part.
All Town Taxi Company (781) 344-9150 90 Lincoln St, Stoughton, Ma.
South Shore Cab & Courier Incorporated (781) 963-2200 21 Tosca Dr, Stoughton, MA.
Vip Taxi of Norwood Incorporated (781) 363-9370 259 Rock St, Norwood, MA.
A & T Taxi (781) 821-9400 825 Washington St, Canton, MA
Viptaxiofnorwoodinc (781) 363-9370 Norwood, MA.