Learn Hardcore Russian: У меня иногда болит нога вечером.

So instead of saying “I hurt my leg” (with я as the subject), Russian treats the body part as the grammatical subject and the person as the possessor: у + (genitive of the person).
This pattern is very common with body parts and health:

У меня болит голова. – My head hurts.
У него болит спина. – His back hurts.

What case is меня in, and why is that case used?

Меня is the genitive singular of я.

The preposition у (“at, by, with”) almost always takes the genitive case.
So:

у меня – at me / I have
у тебя – at you / you have
у неё – at her / she has

In this sentence, у меня indicates possession (it’s my leg that hurts). It’s the same grammatical pattern as у меня есть книга (“I have a book”), just with болит нога instead of есть книга.

Who is the grammatical subject in this sentence – я or нога?

The grammatical subject is нога.

You can see this because:

The verb болит is 3rd person singular.
It agrees in number with нога (leg), which is also singular.

У меня is not the subject; it’s a phrase in the genitive that marks the possessor (“my”). So structurally the sentence is:

(У меня) [подлежащее: нога] [сказуемое: болит].
“(For me) [the leg] [hurts].”

Why is the verb болит in this form, and what is the dictionary form?

The dictionary (infinitive) form is болеть – to hurt, to be ill.

In the sentence we have:

болит – 3rd person singular, present tense.

It matches the subject нога (one leg):

Нога болит. – The leg hurts.
Ноги болят. – The legs hurt.

So you choose болит (singular) or болят (plural) depending on whether you’re talking about one body part or more than one.

Why is it нога, not something like ногу or ноге?

Нога here is in the nominative case because it’s the grammatical subject of the verb болит.

Russian cases:

Nominative is normally used for the subject.
Other cases (accusative, dative, etc.) are used for objects, indirect objects, and different functions.

Since it’s “the leg hurts”, not “I hurt the leg”, the leg is acting as the subject and must be in the nominative: нога болит.

Why don’t we say моя нога иногда болит вечером? Is that wrong?

Моя нога иногда болит вечером is grammatically correct, but the nuance is different.

У меня болит нога. – neutral way to say “My leg hurts.” Very common, focuses on your condition.
Моя нога болит. – puts extra emphasis on the leg itself (“my leg hurts” – as opposed to someone else’s, or as opposed to another body part).

In everyday speech, Russians usually prefer the у меня болит нога pattern for pains and illnesses. Моя нога is possible, just more marked or contrastive in most contexts.

Could we change the word order, for example: Иногда вечером у меня болит нога or У меня болит нога иногда вечером?

Yes, Russian word order is flexible, and these variants are possible:

Иногда вечером у меня болит нога.
Вечером у меня иногда болит нога.

They all mean essentially the same thing. The differences are in rhythm and emphasis:

Putting иногда or вечером at the beginning emphasizes time: “Sometimes in the evening, my leg hurts.”
Keeping у меня at the start is the most neutral for “I sometimes have leg pain in the evening.”

У меня болит нога иногда вечером is understandable but sounds a bit clumsy; adverbs of time like иногда, вечером usually go earlier in the sentence.

What exactly is вечером? Is it an adverb or a noun in a case, and why does it mean “in the evening”?

Вечером is historically the instrumental case of the noun вечер (evening), but in modern usage it functions almost like an adverb meaning “in the evening / during the evening”.

Russian often uses the instrumental case to express a time when something happens, especially with parts of the day:

утром – in the morning
днём – in/at daytime
вечером – in the evening
ночью – at night

So вечером here answers the question когда? (when?) and means “in the evening”.

Where is the stress in the words болит, нога, вечером, меня?

The stress is:

болит – болит (stress on the second syllable)
нога – нога́ (stress on the last syllable)
вечером – ве́чером (stress on the first syllable)
меня – меня́ (stress on the last syllable)

So the whole sentence is pronounced:

У меня́ иногда́ боли́т нога́ ве́чером.

How would I say “My leg doesn’t hurt in the evening” using the same pattern?

You just add не before the verb:

У меня вечером не болит нога. – My leg doesn’t hurt in the evening.

You can move вечером or иногда around as before, but не must stay right in front of болит:

У меня нога вечером не болит.
Вечером у меня нога не болит.

How would I turn this into a yes–no question: “Does your leg sometimes hurt in the evening?”

Russian doesn’t use inversion like English for yes–no questions. You keep the same word order and change intonation:

У тебя иногда болит нога вечером? – Does your leg sometimes hurt in the evening?

You can also add ли for a bit more formality or bookish style, but it’s not necessary here:

Иногда ли у тебя болит нога вечером? – more formal / stylized.

How do I say “My legs sometimes hurt in the evening” (plural)?

You make both the noun and the verb plural:

Singular: У меня иногда болит нога вечером. – My leg sometimes hurts in the evening.
Plural: У меня иногда болят ноги вечером. – My legs sometimes hurt in the evening.

Notice the changes:

нога → ноги (leg → legs)
болит → болят (hurts → hurt, 3rd person plural)