B737-200 ACFT AFTER TKOF; FOLLOWING DEP CTLR HDGS AND ALTS; HAD TCASII CONFLICT WITH AN ARRIVING ACFT. RPTS FROM BOTH FLCS INCLUDED.

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TWR CLRED US FOR TKOF ON RWY 23 WITH A R TURN TO 330 DEGS. AT 400 FT I BEGAN A R TURN TO 330 DEGS. MY FO CONTACTED DEP AND CTLR SAID CLB TO 10000 FT AND MAINTAIN RWY HDG. THE FO SAID CLB TO 10000 FT AND OUR HDG IS 330 DEGS ASSIGNED. DEP CTL THEN SAID MAINTAIN 4000 FT. THE CTLR WAS TALKING FAST AND I WAS HAVING DIFFICULTY UNDERSTANDING HER. I HAD TO ASK THE FO TO CONFIRM THE CTLR'S XMISSIONS AND I HAD TO TURN MY VOLUME CTL UP TO TRY TO UNDERSTAND THE XMISSIONS. THE CTLR NEXT GAVE US A HDG CHANGE TO 290 DEGS. THE CTLR GAVE US A CLB TO 5000 FT. AS WE CLBED; MY FO SAID THE CTLR IS TURNING US INTO THE ONLY TFC IN THE AREA. I ASKED THE FO TO CONFIRM OUR HDG AND ALT. THE CTLR WAS TALKING NONSTOP TO A SMALL AIRPLANE. THE FO FINALLY XMITTED WE WERE 5000 FT HDG 290 DEGS. THE CTLR NEVER RESPONDED. THE TFC KEPT GETTING CLOSER AND THE TCASII GAVE US A CLB AND I INITIATED A CLB. THE OTHER ACFT DSNDED. OUR TCASII SHOWED 2 MI HORIZ SEPARATION AND 600 FT VERT SEPARATION. THE FO TOLD THE CTLR THAT WE HAD CLBED TO AVOID TFC. THE CTLR CLRED US TO 10000 FT; TURN R TO 360 DEGS; AND JOIN THE JETWAY ON COURSE. THIS CTLR CREATED CONFUSION ON DEP BY TALKING TOO FAST; AND WAS EXTREMELY DIFFICULT TO UNDERSTAND. SUPPLEMENTAL INFO FROM ACN 374297: OUR FLT FROM ATL-CAE WAS BEING VECTORED BY CAE APCH CTL FOR A LNDG ON RWY 5 (THIS 'EXPECT' RWY 5 INSTRUCTION; ISSUED BY APCH CTL; WAS CONTRARY TO ATIS INFO ADVISING THE LNDG RWY TO BE RWY 23). WE WERE AT 5000 FT; HDG 050 DEGS; SPD 210 KTS. I NOTICED AN ACFT (VIA THE TCASII) APCHING OUR INTENDED FLT PATH FROM R TO L (ITS HDG; 290 DEGS I THINK). IN ADDITION; THE ACFT WAS CLBING AND APCHING NEAR TO OUR ALT. I DETERMINED THAT WE NEEDED TO CHANGE COURSE AND/OR ALT TO AVOID POSSIBLE CONFLICT. I INSTRUCTED THE FO TO TURN R AND DSND. BOTH ACFT ADVISED APCH CTL OF RA'S AND SUBSEQUENT ALTDEVS.