DC10 CREW FLEW DEP SID VERSUS RWY HDG ON DEP AT LAS. THEY HAD AN NMAC WITH ANOTHER ACFT.

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PER OUR PDC; THE ATC CLRED RTE INCLUDED A SID BUT A FEW LINES BELOW OUR CLRED RTE; IN A DIFFERENT PARAGRAPH; WE WERE INSTRUCTED TO DISREGARD THE 'DP/SID' AND FLY RWY HDG. NONE OF THE CREW MEMBERS CAUGHT THIS AND WITHOUT BEING ASSIGNED A HDG WITH OUR TKOF CLRNC; THE FLC EXECUTED THE SID. AFTER CONTACTING DEP CTL; WE WERE TOLD OF OUR MISTAKE AND GIVEN A HDG AND CONTINUED OUR CLB TO 7000 FT MSL. AFTER LEVELING AT 7000 FT MSL; DEP SAID 'EXPEDITE CLB TO 8000 FT.' SHORTLY AFTER LEVELING AT 8000 FT; DEP TOLD US TO CLB TO 15000 FT AND SAID HE PREVIOUSLY TOLD US 3 TIMES TO CLB TO 15000 FT -- A CLRNC WHICH WE NEVER HEARD. AFTER INITIATING A CLB; WE RECEIVED AN RA TELLING US TO 'MONITOR VERT SPD AND CLB AT 300 FPM.' THE PDC WAS A CONTRIBUTING FACTOR AS OUR RTE CONTAINED A SID AND IN ANOTHER PART OF THE PDC THE CLRNC WAS TO DISREGARD THE SID. ALSO; NOT BEING ASSIGNED A HDG WITH OUR TKOF CLRNC WAS A FACTOR. AFTER REALIZING OUR MISTAKE OF FLYING THE SID WE DID OUR ABSOLUTE BEST AS A CREW TO COMPLY WITH ATC INSTRUCTIONS. ALSO; I FEEL THAT THE USE OF EXCELLENT CRM BY OUR CREW HELPED THIS EVENT HAVE A POSITIVE OUTCOME.