Мне нужно красить мой дом.

Is this correct?
Thanks in advance.

I have to paint my house.
Мне нужно красить мой дом.

I would think something along the line of:

мне нужно покрасить свой дом.

saibot's variant sounds better, but kwatts59 one is right too.
If you decided to paint your house, you should use "мне нужно покрасить". If your friend came to you and said: "Hi, kwatts! Let's get drunk!", when you was painting your house, you should answer "нет, не могу, мне нужно красить дом".

Would надо not sound better here?

Quote:

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Originally Posted by Darobat

Would надо not sound better here?

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I think, "нужно" and "надо" are quite equivalent here.

I've always just used надо with verbs and нужно with neuter nouns.

Quote:

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Originally Posted by Darobat

I've always just used надо with verbs and нужно with neuter nouns.

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At least with verbs you can use "нужно" instead of "надо". Надо is a bit more informal.

В чём разница между ними?

Here's what I can find at the moment:
1. You can't use надо with nouns. For instance, "Мне нужна ручка" is correct, but "Мне надо ручка" is incorrect. OK, sometimes even native Russian may say "Мне надо ручку", but I think, it sounds not very good.
2. Надо is more informal, than нужно. And if you want to reach the height of formality, use необходимо instead of нужно and надо.

Difference between надо and нужно is very insignificant in spoken language.