Remember that the season for road work is whenever there's no snow on the ground. So overall you won't really be able to avoid it.
If you use Google Maps directions, it will show you all of the known road construction points along your route.
Ironically, at the moment there appears to be more road work on the I-70/I-35 route that you used to go to Iowa, than on the I-80/I-76 route.
Note that it's not currently possible to get live traffic data for all of these large stretches of rural highway in the middle of nowhere, though earlier I did see an accident listed on I-80 in western Nebraska on Google Maps, so there is some data available, and road construction is being taken into account when it makes its estimates.
I can tell you from experience that you should always expect delays in and around Omaha, especially if you travel through there on a weekday, but the rest of the trip should not have any significant delays from road work.