How can we clean a dirty interior brick wall?

I googled your question and found several answers to your question. The mortar problem is more difficult as they recommended using muriatic acid which dissolves the mortar. You have to be careful and make sure you wash it off quickly as it will continue to dissolve the mortar in between the bricks. I don't know how easy that would be for you as it is inside brick. You might want to hire a reputable brick layer to come out and do this project or get recommendations from him. Here is the link for that article. http://www.finehomebuilding.com/1999/05/01/removing-hardened-mortar-from-brick

You can use muriatic acid for the mortar- but be very very careful- its dangerous if not. And to clean the rest of the brick: Mix 1 part mild detergent or dishwashing soap and 1 part table salt. Using a sponge, apply the thick paste of cleaning solution you obtained on the brick wall. Scrub the brick wall with a wire brush. Allow the solution to settle in for 10 to 15 minutes. And Use a wet sponge or a cloth to wipe off the cleaning solution. Make sure you rinse the sponge or the cloth on a regular basis in a bucket of lukewarm water. Check that you have removed the cleaning solution entirely. If you notice any remaining cleaning solution on the wall when it is already dry, use a scrub brush and a sponge or cloth to rinse the area. Good luck!!!!

Whatever you use to clean it, try vacuuming it first to remove loose stuff so it doesn't got all over the room.

And cover stuff with drop cloths taped down so the grit and stuff doesn't get under them.

(Yes, I learned those things the hard way.)

And if you use muriatic acid, dispose of it in the toilet rather than the sink. It will stain stainless steel, but shouldn't hurt porcelain or sewage pipes since toilet bowl cleaners often have diluted muriatic acid in them.