In neither case should you use "on", though it would be grammatically correct.

If the man is standing "on" the outside of the house that would suggest to me that he is standing on the vertical walls of the house, like a fly.

If you paint "on" the outside of the house, that suggests to me that you are using the walls like a canvas to produce a painting or mural.

But if you mean that the man is standing on the ground outside your house, or if you mean that you painting the walls a solid colour then you do not use "on".

In neither case should you use "on", though it would be grammatically correct.

If the man is standing "on" the outside of the house that would suggest to me that he is standing on the vertical walls of the house, like a fly.

If you paint "on" the outside of the house, that suggests to me that you are using the walls like a canvas to produce a painting or mural.

On the other hand, if you "paint outside your house" that means you do a painting (on paper?) in the open air outside your house.

But if you mean that the man is standing on the ground outside your house then "Standing outside my house", or if you mean that you painting the walls a solid colour then "painting the outside of my house", with no "on".