Interior brick or exterior brick?

Depending on what kind of brick and the age, pressure washing can work for just dirt/oil.

Paint removal means media blasting(NOT sandblasting!!)

Both sand blasting and pressure washing can inflict severe damage on exterior brick and mortar. The outer surface of brick is hard and highly resistant to water intrusion. Remove it by blasting it away and you expose the much softer interior of the brick. This new surface will absorb water and lead to spalling of the brick.

The kind of discoloration will be part of deciding on a method. There are masonry cleaning chemical for different tasks. Rust, mildew and grease would have separate treatments, for example.

There are more effective wet cleaning tools, like Hot pressure-washers and steam cleaners.

There are abrasive blast cleaning techniques that use softer abrasives than slag or sand, like ground walnut shells, dry ice, baking soda (the last probably better for indoors than for outdoors.)

You need to tell us what you are trying to clean off.

Are we talking about a dirty fireplace or a whole house?

Pictures please.