I also read somewhere that the Republican legislators in one of those states only control their legislature by way of cunning gerrymandering; they won a majority of seats from a minority vote among the electorate.
Most states who's districts are partisan drawn are cunningly gerrymandered. By both parties. It's not limited to one.
In Wisconsin, the lower legislative house (State Assembly) had a popular vote of 54-46 for the Democrats in this election. This resulted in an Assembly split 63-36 in favor of the Republicans, with a net gain of only one seat for the Democrats. In no election since the redistricting in 2011 have the Democrats won more than 39 of the 99 Assembly seats. Wisconsin is gerrymandered so thoroughly that it would take an implausibly huge landslide for the Democrats to have any hope of winning at least the Assembly, and the state Senate is not much different.
Gerrymandering has long been a problem on both sides in most states, but there was some degree of restraint prior to the Republican midterm landslide in 2010. Parties in charge after a census year would give themselves an advantage, but not so extensively and with such attention to detail that the minority party would have no realistic hope of winning a state legislature majority again for the foreseeable future.
Democrats did gerrymander some in the few states they controlled after 2010. Illinois was gerrymandered somewhat, but the effects were minor: the state Congressional delegation was split 12-6 for the Democrats on a 57-41 popular vote in 2012; this turned to 10-8 in 2014 on a 51-49 split. In Maryland, a Republican representative in the western part of the state was knocked off by redrawing his district to extend down to the DC suburbs, turning 6-2 into 7-1. But that's about it - in the places they did have control, the gerrymandering was comparatively minor.
I'm also unaware of any examples where incoming governors and other state-level officials were stripped of much of their power by lame duck sessions if the wrong party happened to win, either. I find it difficult to imagine that anything like this has happened since maybe the Populist-Republican challenge to Democrats in the South in the 1880s and 1890s, although I wouldn't rule out that there could have been something comparable more recently.
Creating a bit of an advantage through gerrymandering and other alterations of the rules is unfortunate but normal. The Republican efforts since 2010 in e.g. North Carolina and Wisconsin have gone far beyond this, though, making it implausible for Democratic legislative victories to happen at all no matter the popular vote numbers. At this point, those states cannot be considered remotely democratic.