Prepare Vegetables: Cut the onion and both peppers into large pieces suitable for skewering. Set aside in a bowl.
Prepare Salmon: Remove bones and skin from the salmon fillet. Cut the salmon into large pieces suitable for skewering.
Make Marinade: In a separate bowl, combine mild mustard, lemon juice from two lemons, olive oil, salt, freshly ground pepper, fresh thyme, and fresh oregano. Mix well.
Marinate Salmon and Vegetables: Add the salmon pieces and cut vegetables to the marinade bowl. Massage gently to coat everything evenly. Let them soak briefly.
Assemble Skewers: Alternately thread pieces of onion, salmon, and peppers onto skewers or straws, folding salmon pieces if thin to fit well.
Grill Skewers: Heat a frying pan or grill to moderate heat. Place three skewers at a time and grill for about 5 to 7 minutes total, turning frequently to cook evenly without burning.
Serve: Serve the salmon straws hot or warm with grilled vegetables, lemon slices, and oregano leaves as garnish.