There's no upper limit for the achievable irregularity if you convert the text to curves (Type > Create Outlines) , ungroup and adjust the placements as you like.
You can also scale, rotate, move and skew letters individually, distort them with the direct selection tool for bizarre effects and apply envelope distort to them. An example:
I guess yo do not aim total randomness. You can keep it look designed if you use only a few tricks, remember their settings and use each of them in the same way to more than one letter.
You can make consistent shifts with arrow keys (set the increment in the preferences) and consistent rotations and scalings with Object > Transform.
Another way to add distortion to a text line is to drag the outlined text to the brushes collection and define it to be an art brush.
Draw with the pen a zigzag or convert a horizontal line with effects to a zigzag path (expand the appearance to make the path free if its zigzagged with effects) and apply the brush to it. Or use only type on path. An example:
You can edit the zigzag after applying the brush. Fix the effect with Expand Appearance.