Cover octopus with cold water in a large pot over medium-high heat. Bring to a boil, reduce heat, and simmer 30 to 45 minutes or until a knife easily pierces the meat. Plunge octopus into ice water, and drain.
Cook calamari in boiling water to cover about 45 seconds to 1 minute, or until rings are opaque. Plunge calamari into ice water, and drain.
Throw away any mussels or clams with open shells. Steam mussels in 1 inch of water 2 minutes or until mussels open. Discard mussels that fail to open. Transfer to a clean bowl; let cool.
Steam clams in 1 inch of water, covered, 3 to 5 minutes or until clams open. Discard clams that fail to open; let cool.
Whisk together oil and next 5 ingredients. Combine seafood in a large bowl. Pour dressing over seafood; toss to coat. Add celery; toss again. Let marinate 2 hours. Divide greens among 6 plates; top with seafood mixture.