B767ER FLC ENCOUNTERS SEVERE TURB AT FL370.

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ON COURSE TOWARD MEMPHIS WITH FINAL DEST ATLANTA. AT FL370 ABOUT 30 NM N OF LIT; WE EXITED A HAZE AND THIN CLOUD LAYER ONLY TO FIND A FEW MI DISTANT A BUILDING; DENSE CUMULOUS CLOUD. RADAR WAS ON; BUT SHOWED NO PRECIP OR TURB INDICATION AND THERE WERE NO RPTS OF MORE THAN LIGHT CHOP. CAPT (MYSELF) WAS AT CTLS AND ASKED THE FO TO REQUEST A 15 DEG DEVIATION N. ZME WAS BUSY TALKING TO OTHER ACFT; SO BY THE TIME WE GOT CLRNC; WE HAD ENTERED THE CLOUD. WE IMMEDIATELY ENCOUNTERED SEVERE TURB WITH ALT GAIN OF 700-800 FT. LASTED 7-10 SECONDS. DISCONNECTED AUTOPLT AND MANUALLY LEVELED OFF AGAIN AT FL370; EXITED CLOUD INTO SMOOTHER AIR. I INSTRUCTED FO TO MAKE TURB RPT TO CTR WHILE I MADE PA TO PAX AND COMMUNICATED WITH FLT ATTENDANTS ABOUT POSSIBLE INJURIES OR DAMAGE. 3 FLT ATTENDANTS HAD MINOR INJURIES. FORTUNATELY; DUE TO PRIOR LIGHT CHOP; THE SEATBELT SIGN WAS ON AND PA HAD BEEN MADE ABOUT 10 MINS PRIOR TO SEVERE TURB FOR PAX AND FLT ATTENDANTS TO REMAIN SEATED WITH SEATBELTS FASTENED. SUPPLEMENTAL INFO FROM ACN 552517: WE EXITED A CLOUD INTO CLR AIR. WE SAW ANOTHER CLOUD AHEAD OF US; BUT NOTHING WAS PAINTED ON THE RADAR. WE TRIED TO GET A HDG CHANGE TO THE L TO AVOID THE CLOUD BUT ATC WAS VERY BUSY. BY THE TIME WE WERE CLRED TO TURN; WE ENTERED THE CLOUD AND EXPERIENCED SEVERE TURB WITH AN ALT GAIN OF 700-800 FT. THE AUTOPLT TURNED OFF. THE TURB LASTED 5-10 SECONDS. WE THEN EXITED THE CLOUD INTO CLR AIR AND DSNDED BACK TO FL370. WE MADE A PA TO THE PAX AND SPOKE WITH THE FLT ATTENDANTS AND FOUND OUT 2 FLT ATTENDANTS HURT THEIR BACKS AND 1 PAX WANTED TO SEE A PARAMEDIC. DURING THE SIT; THE FASTEN SEATBELT SIGN WAS ON AND EVERYONE BUT 1 FLT ATTENDANT WAS SEATED WITH THEIR SEATBELT ON. BOTH FLT ATTENDANTS AND PAX CONTINUED ON WITH US; SO I ASSUME NO ONE WAS SERIOUSLY INJURED.