To make CSS Rules that apply to a specific screen orientation, you'll want the @media rules.
https://www.w3schools.com/cssref/css3_pr_mediaquery.asp
For Monogatari, you can use the same rules that are used to make the Quick Menu appear at the top in portrait mode and at the bottom in landscape mode. Then to affect the side image div container, you would select it with div[data-content="side-image"]
@media screen and (max-width: 37.56255em) {
div[data-content="side-image"] {
/*whatever rules you want here.*/
}
}
From there experiment with setting a width or whatever you need to get the game to look the way you want it to!
As for the other thing you mentioned, about the data-expression property, that's a property that is applied to the entire text box based on specific expressions shown in the side image. This allows you to do things like stylize the entire text box based on if they are angry or sad or whatever. Like make the whole text box shake when you pull up the "seething" expression or something. Here's a quick little demo I slapped together back when that feature was first added. http://newrem.com/monogatari/dynamicSideImages/