I see a lot of posts about draft strategy (obviously), but all of the advice is geared toward a league in which the majority of people know what they are doing. Most of us are probably also in a league or two in which not as many of the owners are as "into" it as we are. I've found there needs to be slight differences in draft approach if you want to keep your bragging rights in these leagues.
Casual Players will draft QB's and defenses earlier than you. There are a couple implications here. The biggest of them is that waiting for a QB may no longer be a viable strategy. If 6-8 people in the league plan on taking a backup QB before you plan on taking your first, you are going to be stuck with a QB way farther down on your rankings than you thought. When defenses are drafted so early, more players you are targeting in the late rounds will fall to you, which is important because...
Stockpiling at RB and WR early is not as necessary as in a competitive league. That's not to say you shouldn't get a good stock of those players, but it is much better in a casual league to get the elite players at each position. This is because 1: more of your favorite sleepers will be available later in the draft. 2: they won't trade with you. Having 5 great WR's is worthless if they sit on the bench and nobody will trade with you because of either apathy or the assumption that you are trying to rip them off. And 3: They won't be paying attention to the waiver wire, so you have a much better shot at good pickups throughout the season.
Know the people in your league. Casual players are much more influenced by things that are not very relevant. Look for owners who love a certain team and are biased, or want players who graduated from the same college, or even stranger things.
Hope you found this interesting, these are just my observations