Can I say "I have several homework"?

Ideas can be expressed in many different sentence forms in English, but your sentence choice is incorrect for two reasons: (1) homework is an uncountable noun and (2) several is a quantifier that cannot be used with an uncountable noun.

Uncountable nouns are those that refer to something as an indivisible group or quantity; they are also called mass nouns because they refer to large masses, quantities or amounts of something. For example, furniture, advice and luggage are uncountable mass nouns, which are used in the singular form because a plural form is unavailable for use, that refer to all of something thought of or to a single piece of something: 

• The air-carrier porters hauled the luggage, all 2,000 pieces of it, to the airplane.


• The airport porter told him to check his luggage, even though he had only one piece of it, at the check-in desk.

Uncountable mass nouns can be modified by a select few quantifying determiners. In contrast, countable nouns, those nouns that have plural forms (e.g., one horse, 500 horses, two horses) and are thus said to be countable, can be modified by a different selection of quantifying determiners. Some important kinds of noun quantifiers answer the questions: How many/much? How many/much more? How many/much fewer/less?

Uncountable nouns answer these questions with the quantifiers: much (How much?), much (How much more?), and less (How much less?).

In contrast, countable nouns, those that can be pluralized hence counted, answer these questions with different quantifiers: many (How many?), many or several (How many more?), and fewer (How many less?). 

Looking at this, we see that the quantifying modifier "several" belongs with a countable noun, like cats or pencils or cars (i.e., many or several cats, many or several pencils, many or several cars). Since "homework" is an uncountable mass noun, having no possibility of pluralization, "several" cannot be used to modify "homework": "several homework" in not grammatical because of (1) the uncountability of the noun and because of (2) the prescribed association of different modifying quantifiers with uncountable (mass) and countable (pluralizable) nouns. 

The simple change from the countable noun quantifier "several" to the correct uncountable noun quantifier "much" will make your sentence grammatical: not "I have several homework" but "I have much homework." This then answers "How much homework do you have?" You answer, "I have much homework." [You can also answer, among other things, "I have little homework" or "I have some homework."]