A CPR HAWKER CAPT; FLYING AT FL330 ENCOUNTERED WAKE TURB FROM A B757 2000 FT ABOVE AND A B777 AHEAD AND CLBING.

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ACFT DEPARTED DCA ON 3 PAX FLT TO IXD (OLATHE; KS). ZDC VECTORED ACFT TO JOIN J134 AND ASSIGNED ALT FL330. CTR ADVISED THAT WE WERE IN TRAIL OF A COMPANY A B777; ALSO AT FL330. CREW OBSERVED B777 AT 12 O'CLOCK POS; WELL AHEAD. SUBSEQUENT ZDC XMISSION WAS INTERPRETED BY CREW TO EXPECT CLB TO FL350 BEFORE CLB CLRNC WOULD BE PROVIDED TO B777. AFTER A FEW MINS; B777 WAS OBSERVED TO BE AT 12 O'CLOCK POS; CLBING. AT THIS TIME; ZDC ADVISED OF XING COMPANY B757; L TO R; AT FL350. THAT ACFT WAS ALSO SIGHTED ON CONSTANT BEARING/DECREASING RANGE. UP TO THIS TIME; FLT WAS IN SMOOTH AIR. HOWEVER; FL WINDS WERE JUST 7-10 KTS FROM OUR 7-8 O'CLOCK POS. PIC SUSPECTED POSSIBLE ENCOUNTER WITH B777 WAKE TURB WAS IMMINENT; BUT TURN UPWIND WOULD PLACE ACFT 2000 FT BELOW CONVERGING B757 WAKE. COURSE WAS MAINTAINED UNTIL ACFT WAS APPROX 1 MI B757; THEN; A SHALLOW L TURN COMMENCED; MODERATE TURB ENCOUNTERED; FOLLOWED BY UNCOMMANDED L ROLL TO APPROX 30 DEG ANGLE OF BANK. ENCOUNTER LASTED APPROX 5 SECONDS BEFORE LEVEL; SMOOTH FLT CONDITIONS REGAINED. (AUTOPLT DID NOT DISCONNECT.) CREW RPTED ENCOUNTER TO ZDC AND MAINTAINED OFFSET 2 NM S OF AIRWAY UNTIL B777 COURSE DIVERGED OVER ZTL ADVISED THAT WE WERE 12 NM IN-TRAIL OF B777.