Statement I: Methyl orange is a weak base, not a weak acid.

This is because Methyl orange is actually a pH indicator commonly used in titrations. In its deprotonated form, it appears yellow, and in its protonated form, it appears red. Methyl orange has the ability to accept a proton ($H^+$) from water (a characteristic of a base) and is therefore considered a weak base.

Chemically, this can be represented as:

$$\text{MO}^- + \text{H}_2\text{O} \leftrightharpoons \text{MOH} + \text{OH}^-$$

Here, $\text{MO}^-$ is the methyl orange anion, $\text{MOH}$ is the protonated form of methyl orange, and $\text{OH}^-$ is the hydroxide ion.

Statement II: The quinonoid form of methyl orange is more intensely colored than the benzenoid form.

Methyl orange exists in two resonance forms: a benzenoid form (yellow) and a quinonoid form (red). In acidic solution, the equilibrium shifts towards the quinonoid form, which is red and more intensely colored than the yellow benzenoid form.

The equilibrium can be represented as follows:

Yellow Benzenoid form $\leftrightharpoons$ Red Quinonoid form

In conclusion, both statements are incorrect. Methyl orange is a weak base and the quinonoid form is more intensely colored. So, the correct answer is option A. Both Statement I and Statement II are incorrect.