Do I need to eat more calories to get stronger?

Strength is called a neurological (rather than physiological) response because in general, you can gain strength simply by training your central nervous system to become more efficient at contracting more motor units simultaneously. This allows you to generate more force without more mass.

It is a myth that strength and mass go hand in hand. They do not - they impact each other but not to the greater extent. Some of the strongest power-lifters in the world have smaller muscles than many bodybuilders, and some of the biggest bodybuilders have weak bench press and squats.
It is true that gaining muscle requires a caloric surplus and losing fat requires a caloric deficit. People who just start out have an adaptive response and can gain muscle while losing the fat. After your first several months, however, you are pretty much in that mode.

Most people who lose fat and gain muscle within a given period - for example, bodybuilders preparing for a competition - are doing it in waves, i.e. a few higher calorie days and a few lower calorie days, so they are in a surplus/deficit within smaller units of time. Even people who consume constant nutrition and pull this off tend to manipulate cardio and nutrition so if you look at a "window" of time, they are doing one or the other (surplus or deficit) but it averages to a net effect over time.