In large bowl, whisk together oil, vinegar, mustard, garlic, salt and pepper.
Cut eggplant in half lengthwise; cut crosswise into 1/2-inch (1 cm) thick pieces and add to bowl. Cut red and yellow peppers and onion into 1-inch (2.5 cm) pieces; add to bowl. Add tomatoes; toss to coat. Let stand for 10 minutes.
Meanwhile, prick sausages with fork. Place on microwaveable plate; cover and microwave at high until no longer pink inside, 5 minutes. Cut into quarters.
Onto 8 metal or soaked wooden skewers, alternately thread sausage, eggplant, red and yellow peppers, onion, tomatoes and artichoke hearts. (Make-ahead: Cover and refrigerate for up to 4 hours.)
Place skewers on greased grill over medium-high heat; close lid and grill, turning once, until browned and vegetables are tender, about 10 minutes