For a single style attribute, you can use the following syntax:
<div [style.background-color]="style1 ? 'red' : (style2 ? 'blue' : null)">
I assumed that the background color should not be set if neither style1 nor style2 is true.
Since the question title mentions ngStyle, here is the equivalent syntax with that directive:
<div [ngStyle]="{'background-color': style1 ? 'red' : (style2 ? 'blue' : null) }">