Any potential location clues that might help? Often knowing that your father was born, let's say, in the midwest might be useful to start paring down the information. Or approximate ages or dates? From the oldest child, I usually drop back 20 years or so, with a tolerance range of + or - 5 years, and start searching.
So my process on finding unknowns is to start providing my best guesses to narrow down the search, and it generally either proves or disproves my assumptions. If I do half dozen searches with the wrong assumptions and I get nothing or end up on a wild goose chase, I figure I learned to at least eliminate that path for now and to hunt in a different direction. Occasionally this is a bad way to go, as it involves leaping to a judgment and such, but I find that at least 50-60% of the time, I discover something useful - either in the negative or positive.