B737 FLC RECEIVED MULTIPLE HDG AND ALT CLRNCS DURING TKOF AND INITIAL CLB. WHILE RESOLVING TCASII RA; AN ALTDEV OCCURRED.

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B737-300 OKLAHOMA CITY TO DALLAS. TKOF WAS ON RWY 31. WX WAS NOT A FACTOR. TKOF CLRNC WAS FLY HDG 010 DEGS AND CLB TO 5000 FT AND TWR ADVISED THAT A LIGHT ACFT WAS ORBITING N OF THE FIELD VFR. THE FO ASKED TWR IF THEY STILL WANTED US TO FLY A 010 DEG HDG. TWR CONFIRMED A 010 DEG HDG. AFTER TKOF; DURING THE TURN TO 010 DEGS; TWR AMENDED THE ALT CLRNC TO 4000 FT. DEP SUBSEQUENTLY ISSUED HDG OF 070 DEGS AND THEN 090 DEGS. TWR DID NOT GIVE ANY FURTHER CALLS ABOUT THE LIGHT ACFT TFC. AT ABOUT 3000 FT; THE CAPT ENGAGED THE AUTOPLT IN THE COMMAND MODE WITH 4000 FT IN THE ALT CLRNC WINDOW (AUTOMATIC ALT ACQUIRE WAS ARMED). APCHING 090 DEG HDG AND 4000 FT; A TCASII TA/RA ANNOUNCED 'REDUCE VERT SPD.' THIS WAS THE FIRST WARNING OF POTENTIAL TFC CONFLICT. THE CREW DIVERTED THEIR ATTN TO THE TCASII AND ACQUIRING THE SECOND ACFT VISUALLY. AT THE TCASII ALERT; THE LIGHT ACFT WAS DIRECTLY ON OUR NOSE AND ABOUT 1300 FT HIGH. BOTH THE CAPT AND FO GAVE THE POP UP TFC TA/RA OUR UNDIVIDED ATTN. THE CREW PICKED UP A VISUAL ON THE LIGHT ACFT WITHIN 5 SECONDS (AT 12 O'CLOCK; 3 NM; SLIGHTLY HIGH) AND VERIFIED THAT ADEQUATE SEPARATION EXISTED. WHEN THE CREW LOOKED BACK INSIDE THE COCKPIT AT ALT FOLLOWING VISUAL ACQUISITION OF THE LIGHT ACFT; BOTH THE CAPT AND THE FO REALIZED THAT ALT HOLD HAD NOT ENGAGED; AND THAT OUR ACFT HAD CLBED THROUGH THE ASSIGNED ALT BY 400 FT TO 4400 FT. THE CAPT IMMEDIATELY CORRECTED THE ALTDEV -- DSNDING BACK DOWN TO 4000 FT. THE LIGHT ACFT PASSED DIRECTLY OVERHEAD AS WE DSNDED TOWARDS 4000 FT AND AT THE SAME TIME; DEP CTL DIRECTED US TO MAINTAIN 4000 FT. THE MINIMUM ACFT SEPARATION WAS APPROX 1000 FT. AT NO TIME WAS ANY EVASIVE ACTION REQUIRED OR TAKEN. LESSONS LEARNED: THIS CAPT AND FO LEARNED THAT EXTRA ATTN TO ACFT PARAMETERS IS REQUIRED DURING TCASII EVENTS TO PREVENT ALT; AIRSPD; OR HDG DEVS WHILE THE CREW'S ATTN IS DISTR. THE TCASII ALERT; AS WE WERE ROLLING OUT AND LEVELING OFF; WAS TOTALLY UNEXPECTED AND DIVERTED OUR ATTN AWAY FROM MONITORING THE LEVELOFF. THIS INITIALLY CAUSED US TO MISS THE FACT THAT THE AUTOPLT DID NOT ACQUIRE THE 4000 FT ALT AND LEVELOFF. FOLLOWING THE TA/RA; WE REFED THE TCASII SCOPE AND THEN LOOKED OUTSIDE; WE FELT THAT THE MOST CRITICAL ACTION AT THAT MOMENT WAS TO GET A TALLY ON THE LIGHT ACFT AND TO VISUALLY GUARANTEE SAFE SEPARATION. FROM THE VIEWPOINT OF AIR TFC CTL; WE BELIEVE THAT IT WOULD HAVE BEEN POSSIBLE TO COMPLETELY AVOID ANY POSSIBLE ACFT CONFLICT BY VECTORING OUR ACFT TO STAY LATERALLY CLR OF THE LIGHT ACFT. VECTORING US W AND THEN S OR FURTHER TO THE N BEFORE TURNING E WOULD HAVE TOTALLY AVOIDED THE POSSIBILITY OF ANY TCASII ALERTS OR ACFT CONFLICTS. ADDITIONALLY; HAD ATC POINTED OUT THE LIGHT TFC AS WE CLBED OUT; WE COULD HAVE ATTEMPTED TO PICK UP A VISUAL PRIOR TO ANY TCASII ALERTS. HAVING A VISUAL PRIOR TO THE TCASII TA/RA WOULD HAVE ALLOWED THE FO TO NOTE THE ALERT AND QUICKLY CONFIRM THAT WE HAD VISUAL ON THE TFC WHILE THE CAPT CONTINUED TO FLY THE PARAMETERS ASSIGNED BY ATC.