First, it starts with a cup of coffee, then turning up the volume with your favorite WWII music or modern hard rock equivalent thereof. After some SOS with a side order of bacon, and a fresh refill, one loads the scenario - skips the turn replay because all of the good stuff is at the end. Smart opponents always start moving units in areas other than the important areas. Watching the 8,000 movement replay has a low return -- one therefore assumes the worst case is happening everywhere. If it didn't happen this turn... it'll certainly be next turn.
From there, it is mainly a matter of continuous lines and zones of control, force preservation where possible, prioritizing reinforcements and concentrating force as needed. Same as smaller games.
Everyone has their own preferences. There are lots of smaller games out there, not quite as many monsters. TOAW's awesome because it has something for everyone.
I tend to like the monsters, for much the same reason as the Campaign series has linked campaigns in addition to scenarios, or perhaps from a different angle - why people like World of Warcraft, the long-term evolution of things.
The monsters then are like lots of small scenarios wrapped up into one - interconnected, where what happens in one area can impact another. Within these kinds of frameworks, taking an objective -- Warsaw, Kharkov, Moscow, Baku, Paris or Berlin is somewhat less important than being able to "survive the experience".
But it is the somethin' for everyone thing that makes TOAW + 15 years a lot more than perhaps it was intended to be and with some extra effort - perhaps CAN be. The original TOAW was a lot like a great double cheeseburger. Now... it's like a great double chili cheeseburger with lots of onions and a heaping side order of jalapenos with a frosty mug of beer - and a keg or two of that waiting behind it. TOAW may never be perfected, by the time it is, our standards for it will have changed.