Drywall – Fixing awkward gap between drywall and brick

Absolutely do not use an expanding gap filler, it will make matters worse. If you have verified that each step is level so that it doesn't need to be re-secured to the tread than the gaps can be filled. Also verify that the steps are not loose or shifting.

The easiest and most used product to fill each gap would be a latex caulking. A cartridge (or tube) is placed in a caulking gun and applied in a continuous bead along the gap. Once the gap is covered press it into the gap with a putty knife. This will also flatten the caulking so that it conforms with the flat wall. A very damp rag will wipe up any wayward caulk that didn't get pushed into the gap.

It will take about 24 hours for the caulk to fully cure. It than can be painted if desired, but there are plenty of colors to choose from which may not make painting needed.

As been suggested by a prominent authority well versed in caulking and fully supported by myself, you must be sure to use a Latex-type caulk. Not to be confused with a 100% silicone or a urethane caulking. Latex is easier and more forgiving than the other types.

I would consider putting molding around the door and turning over the face of the brick. I would use a jamb-like board perpendicular to the wall and the door, and make its width flush with the face of the brick. Then add a small flat board parallel to the wall overhanging the door side of the jamb by about 1/8 inch and the brick just wide enough to cover the broken edges (maybe 1 1/2 inches). Paint it to match the door and it will look like part of the door frame.

I would fill the gaps between the door and brick with exterior foam sealant. Just be careful since this expands and you don'r want so much that it warps the door frame. Apply it, trim it flush, then do the molding.