Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Flight Crew Total 18000
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Human Factors; Chart Or Publication; Procedure
We were flying the TYNEE ONE RNAV arrival with many weather deviations and weather avoidance vectors.  Once clear of weather;  ATC cleared us direct to ODERY; which we heard as RODDE.  ATC advised us that we were south of course and issued a vector to join final for Runway 24.Flew a visual approach and landed uneventfully.The fix names ODERY and RODDE are too similar sounding over the radio/cockpit noise.  Clearences to these fixes either need to be phonetically spelled out or the names changed to something less similar sounding.
An air carrier crew flying the RSW TYNEE ONE RNAV were cleared direct ODERY but heard RODDE; 5 NM from ODERY because they were phonetically similar on the radio.