Well it's impossible to answer that without knowing if you have anyone that is hitting hotter on your bench. I would have alot more patience with Giambi, he is the best 1B in baseball and will put up huge numbers for you. Konerko is also a very solid 1B, in the top 10 at least and good for a .300 average, 30 HR and 100 RBI.
I would put Giambi in the lineup, both because he is a better hitter overall than Konerko and because of the lifetime stats that you mentioned. Also, unless you are using Konerko in a utility slot, he is a very solid player that is basically being wasted if you have Giambi too. You could trade Konerko for an upgrade at another position.
Edgar might put up nice injuries but he is also a huge injury threat so I wouldn't count on him playing more than 120 games.
The past three years, Konerko has hit 95+ RBI and had an average of .285 or higher. There is no reason to think he won't hit those levels unless he gets hurt. He is also a notoriously streaky hitter, as you noted, with 71 RBI the first half of the season and then only 33 the second half. Overall, though, his numbers should be very good.
uhh....that Giambi kid you mentioned...you said Jason right? Now, he might not be off to the hottest start in the world, but uhh, he really doesn't suck, so I'd just leave him in there and suggest to you that by the end of the year you won't complain about the numbers he's produced for ya.
Last thing you want is him sitting on your bench when he finally breaks out.
"You can observe a lot just by watching."