Use Multiple Channels
Face-to-face communication is only one way to convey the message. Address how tasks tie to strategy in written communication as well. When you create a project charter, state how the project's objectives meet company and department goals. When you develop release criteria, include an explanation of how the criteria relate to market and revenue goals.
It's an Investment
It's not as if you didn't already have enough to do, is it? And now I'm suggesting you take more time to communicate company strategy to everyone on your team. It is an investment, which will save you time in the future. You'll spend less time backtracking, you'll remove yourself as a communication/decision-making bottleneck, and you'll begin to see people function more independently. When people understand how their work fits in the big picture, they'll be better equipped to make decisions and set priorities.