I don't think it's the worchester sauce that caused the problem, more likely it's the fat spatter from the chicken and the vegetable oil that has built up and started to smoke. The worchester sauce may have added to the smell but it's not what actually caused the problem.
You should clean your oven more regularly, it's a safety thing as much as to prevent smoking - you don't want a fat fire in your oven! There's 2 options there, you could heat it off (either at high temperature or a self clean if it has one) or you can use a chemical oven cleaner. If your oven is greasy enough to smoke up your house I'd recommend you get an oven cleaner and scrub - it's messy but it will clean your oven without choking up your house with smoke.
BTW, you shouldn't need to add oil when baking your chicken as there's enough fat already.