Air India Limited, IndiGo Airlines and 2 other airlines fly from New Delhi to Cuttack hourly. Alternatively, Indian Railways operates a train from New Delhi to Cuttack once daily. Tickets cost $30 - $45 and the journey takes 23 h 25 min.
From New Delhi Metro to Delhi airport, fly to Bhubaneswar airport, then taxi to Cuttack. 3 h 49 min $188. From New Delhi (NDLS) train to Cuttack (CTC). 23 h 25 min $37. From New Delhi drive to Cuttack. 22 h 8 min $201.