In a bowl, combine the first four ingredients to create an olive oil mixture.
Toss the quartered potatoes with 1 tablespoon of the olive oil mixture.
Toss the squash, onion, and bell pepper with the remaining olive oil mixture.
Place the potatoes in a grill wok or a metal basket that has been lightly greased.
Grill, covered with the grill lid, over medium-high heat (350° to 400°) for 10 minutes.
Add the squash, onion, and bell pepper to the grill wok or basket.
Grill while tossing occasionally for an additional 15 minutes or until the potatoes are tender.
Combine the softened butter and oregano, then add this mixture to the grilled vegetables, tossing to coat evenly.
Serve immediately.