The group of 12 given to Sir John Hackett were among artefacts taken on July 3, and the local council and the Queen's Royal Irish Hussars Museum Collection, based at the Redoubt, have jointly offered a £2000 reward to recover them and convict those responsible.
In 1941 Sir John (1910-97) had earned the MC in the Syrian campaign, and was wounded. Service in the Western Desert brought him the DSO (and another wound).
He raised the 4th Parachute Brigade, which he commanded in Italy and North Africa and then led in the ill-fated Market Garden operation.
At Arnhem he was severely injured by a shell splinter after fighting alongside his men in hand-to-hand combat. A South African surgeon saved his life and he escaped, hidden for a while by a Dutch family who risked their lives.
Post-war service included commanding the 20th Armoured Brigade and the post of General Officer Commanding-in-chief of Northern Ireland. In 1945 he was given a bar to his DSO and further awards included an MBE and CBE, KCB and GCB.
Jonathan Seaman, museum officer at Eastbourne Borough Council, said: "The loss of General Hackett's medal group really does feel like the desecration of a great war hero's memory.
"This was a person who went above and beyond the call of duty on numerous occasions during the Second World War, including being seriously wounded and captured at Arnhem as part of Operation Market Garden, only to escape while still swathed in bandages to rejoin the war effort later."
A Russian bugle from the scene of the Charge of the Light Brigade was also taken.
The Eastbourne theft is the latest in a long line of museum break-ins during the past six months.