DA20 TAXIS ON CLOSED RWY VICE TXWY E AT CYHU.

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AFTER PROCESSING THROUGH CUSTOMS WE CONTACTED GND CTL TO TAXI TO PARKING. GND CTL CLRED US TO TAXI FROM CUSTOMS VIA 'T;' 'RWY 28;' 'L' HOLD SHORT OF RWY 24R ON 'L.' WE HELD SHORT OF RWY 24R AT 'L' FOR ABOUT 2 MINS FOR LNDG JET TFC. ONCE THE ACFT LANDED IT HELD SHORT OF 'L' SINCE THEY NEEDED TO UTILIZE THE TXWY WE WERE ON. THE GND CTLR THEN FURTHER CLRED US TO TAXI VIA 'C' HOLD SHORT OF RWY 24R ON 'C' AT THE RWY 24R THRESHOLD. WE TAXIED STRAIGHT AHEAD ON 'L;' PASSED THE TFC WHILE XING RWY 24R AND MADE A R TURN ON 'C.' THE ISSUE WAS TXWY 'L' IS NOT DESIGNATED A TXWY LEADING TO 'C.' BEYOND RWY 24R; 'L' IS A PORTION OF A CLOSED RWY. THE GND CTLR TOLD US WE SHOULD HAVE UTILIZED 'E' INSTEAD OF THE CLOSED RWY SINCE THIS WAS NO LONGER A VALID TXWY OR RWY. THAT PARTICULAR INTXN AT CYHU IS CONFUSING BECAUSE THE ABANDONED RWY COULD EASILY BE CONFUSED AS A TXWY. OUR COMPLETE ATTN TO THE TXWY DIAGRAM; BETTER SIGNAGE INDICATING THE CLOSED RWY; AND SPECIFIC INSTRUCTIONS TO TAXI VIA 'E' COULD HELP PREVENT ACFT FROM TAXIING ONTO THE CLOSED RWY.