"A man is standing outside/on the outside of my house"

Question

"A man is standing outside of my house" or "A man is standing on the outside of my house"?

"I will paint outside of my house" or "I will paint on the outside of my house".

Could you pls tell me if I Should use "On the" or not?

Answer 1

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".

Answer 2

Question: "A man is standing outside of my house" or "A man is standing on the outside of my house"? [buzzer]

The first is OK, but we would shorten it:
A man is standing outside my house.

"I will paint outside of my house" or "I will paint on the outside of my house".

Neither of those really work for this meaning:

I will paint the outside of my house. [as opposed to the inside walls]

outside can be a noun: the outside of my house OR an adverb of place: I am outside my house.

It can also be a preposition or adjective. But I am only giving examples for the question here.

Answer 3

1. A man is standing outside of my house
2. A man is standing on the outside of my house.
3. I will paint outside of my house
4. I will paint on the outside of my house

Eliminate ‘on the’ in sentence 2, and eliminate ‘of’ in sentences 1-3.
Sentence 3 “I will paint outside my house” suggests that the speaker is doing a painting outdoors.
In sentence 4, also eliminate on, but leave the preposition of .

4. I will paint the outside of my house

Cambridge Dictionary provides this example

The outside of the house needs painting.

and includes the following notations

Outside

Outside is an adverb, an adjective, a preposition or a noun.

We use outside as an adverb or an adjective to mean ‘not in a building’:
“It was sunny outside, but not very warm.” (adverb)
“It’s a bit dark at night. We could put an outside light there.” (adjective)
[…]
Outside as a noun is used to refer to the exterior of something. It is more informal than exterior:
“The outside of the house is not very attractive, but inside it is beautiful.” (or, more formal, The exterior of the house …)

Interesting to note that a number of sources; here and here, claim that “outside of” is American English while British English speakers will generally not use ‘of’
e.g. …outside of the city… (US)

OK, we think “outside the hotel” is more elegant, but we don’t think “outside of” is wrong here, and neither, apparently, do most Americans.” […] the dictionary [OED] recognizes “outside of” as entirely normal when used in the spatial sense, defined as “beyond the walls, limits, or bounds of; to or on the outside of; external to.” Grammarphobia.com

Perhaps the scenario below will help to clarify

Aiko: Where are you?
Benjiro: I'm [standing] outside [your house].
Aiko: Why did you come without warning me? I'm so embarrassed. My house needs to be repainted.
Benjiro: It's not that bad. I'll paint the outside walls if you like.
OR
Benjiro: Next week I'll come over and help paint the façade

Answer 4

As OP's four sentences convey different meanings, I have separated them:

1."A man is standing outside of my house" or
2.A man is standing on the outside of my house"?
3."I will paint outside of my house" or.
4."I will paint on the outside of my house".
Could you pls tell me if I Should use "On the" or not?

The explanation is based on my understanding of your intended meaning,.

In the first sentence "of" is redundant
1."A man is standing outside my house." conveys the same meaning.

The second sentence lacks clarity. This sentence will give a clear meaning (if this is the intended meaning).
2."A man is leaning against the wall outside my house.

Third sentence: I guess the intended meaning is the painting of the house itself, it can be rephrased as (it can also mean you will get your wall painted by employing someone).
3.I will paint the outside of my house.
Or
I will paint the exterior of my house."

Sentence 4 : Intended meaning - You are an artist and you wish to work outdoors. "on a canvas" can be added for clarity but is not necessary if others know that you are an artist.:
4. I will paint (on a canvas) outside my house.

Summary: avoid using unnecessary prepositions as they can lead to confusion.