DURING ACFT TRANSITION LNDG PRACTICE; THE PLTS FORGOT TO OBTAIN LNDG CLRNC.

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I WAS FLYING WITH A STUDENT PLT HELPING THEM TRANSITION TO A 'NEW' AIRPLANE -- THIS WAS A PA28-161. THEY WERE PREVIOUSLY TRAINING IN A GRUMMAN. WE DID MANEUVERS FOR ABOUT AN HR THEN CAME BACK TO PEASE TO LAND. THERE WERE STRONG WINDS 19-23 KTS -- ALMOST A DIRECT XWIND. WE HAD BEEN ASKED BY TWR TO RPT DOWNWIND; WHICH WE DID; BUT THEN WE PROCEEDED AROUND THE PATTERN TO BASE AND THEN FINAL. BOTH OF THESE LEGS GOT VERY BUSY IN THE COCKPIT AND WITH EVERYTHING HAPPENING SO QUICKLY; WE FORGOT TO ASK IF WE WERE CLRED TO LAND AND PROCEEDED TO TOUCH DOWN. AT THIS POINT; TWR ASKED US 'WHICH TWR HAD GIVEN US PERMISSION TO LAND.' AT THAT MOMENT; THE STUDENT AND I REALIZED OUR MISTAKE. WE REALIZED THE POTENTIAL SAFETY PROB; AND WERE HORRIFIED AT WHAT HAD OCCURRED. FORTUNATELY; WE WERE THE ONLY AIRPLANE IN THE TFC PATTERN; ALTHOUGH THAT FACT PROBABLY CONTRIBUTED TO OUR ERROR. CONTRIBUTING FACTORS MAY HAVE BEEN: STUDENT UNFAMILIAR WITH AIRPLANE AND NEEDING EXTRA HELP. I USUALLY FLY OUT OF NON TWRED ARPTS. IN THE PAST I HAVE ALWAYS HAD TWR 'VOLUNTEER' THE CLRNC TO LAND WITHOUT MY HAVING TO ASK FOR IT. THE STRONG WINDS CAUSED ME TO NEED TO DEVOTE EVEN MORE ATTN TO HELPING THE STUDENT CTL THE PLANE SAFELY SO I WAS FURTHER DISTRACTED FROM GETTING THAT CLRNC. I DO KNOW THAT I AM SUPPOSED TO KNOW BETTER. A POTENTIAL CORRECTIVE ACTION WOULD HAVE BEEN FOR ME TO REMEMBER TO ASK 'ARE WE CLR TO LAND.' OF COURSE; I WAS DISTR FROM THE DUTY OF RADIO BY THE TASK OF HELPING THE STUDENT 'FLY THE AIRPLANE NO MATTER WHAT.' ANOTHER ACTION COULD HAVE BEEN FOR THE TWR TO CLR US TO LAND SINCE WE WERE; TO MY KNOWLEDGE; THE ONLY AIRPLANE USING THAT ARPT AT THAT TIME. IN OTHER WORDS; THEY COULD HAVE SEEN US COMING; AND AS MOST TWRS DO; PROVIDED US THE CLRNC AUTOMATICALLY.