Learn Hardcore Russian: В этом месяце у меня был сильный стресс на работе.

Russian usually doesn’t use a direct equivalent of English to have in everyday speech.
Instead, possession or experiencing something is expressed with the construction:

у + [person in genitive] + есть/был/будет + noun (in nominative)

Literally, у меня был сильный стресс is like “at me there was strong stress”, which corresponds to “I had strong stress” or more naturally “I was under a lot of stress.”

Using я имел стресс sounds very unnatural here; иметь is used, but mostly in formal, abstract, or set expressions (e.g. иметь значение – to have significance).

Why меня and not мне after у?

У always takes the genitive case.

я (I) → меня in the genitive
мне is the dative form, used for to me / for me, not after у.

So:

у меня = at me / I have
у тебя = you have
у него = he has, etc.

Using у мне would be grammatically wrong in Russian.

Why is стресс in the nominative and not стресса (genitive) after у меня был?

In у меня был сильный стресс, the logical subject of the sentence is стресс.

The pattern is:

у + genitive (person) + есть/был/будет + noun in nominative

Examples:

У меня есть машина. – I have a car.
У неё был отпуск. – She had a vacation.
У нас будет экзамен. – We will have an exam.

So стресс must be in the nominative:
у меня был сильный стресс, not стресса.

Why is it был and not была, было, or just no verb at all?

Agreement:
Был is masculine singular past tense of быть (to be).
It agrees with the noun стресс, which is masculine:
- был стресс (masc.)
- была проблема (fem.)
- было чувство (neut.)
Why we can’t omit it here:
In the present tense, Russian usually omits есть:
- У меня сильный стресс. – I’m under a lot of stress (now).
But in the past tense, you normally must use the past form:
- У меня был сильный стресс. – I was under a lot of stress. Without был, it sounds like present, not past.

So был is required here and must match стресс in gender and number.

Why is в этом месяце (prepositional) used instead of в этот месяц?

В этом месяце uses the prepositional case to express time within a period:
in this month / during this month.

в этом месяце = during this month, at some time this month

В этот месяц (accusative) is possible, but is:

much less common
used mostly in emphatic or contrastive contexts, like “in this particular month (and not another one)”.

For a neutral “this month” as a time frame, you almost always say:

В этом месяце у меня был сильный стресс на работе.

Could we change the word order, like У меня в этом месяце был сильный стресс на работе? Does it change the meaning?

Yes, you can change the word order; Russian is flexible that way. The basic meaning stays the same, but the focus can shift slightly.

Possible variants:

В этом месяце у меня был сильный стресс на работе.
Neutral, standard; sets the time frame first: This month, I had a lot of stress at work.
У меня в этом месяце был сильный стресс на работе.
Slightly more focus on у меня (it was me who had this stress this month).
У меня был сильный стресс на работе в этом месяце.
Puts в этом месяце at the end, which can sound like you’re adding the month as extra detail.

All are grammatically correct; the differences are about emphasis, not about core meaning.

Why is the adjective сильный used with стресс? Can I say большой стресс or something else?

With стресс, сильный стресс is a very natural collocation meaning strong, intense stress.

Other options:

сильный стресс – strong/intense stress (very common)
большой стресс – literally big stress; less idiomatic, but can be used
серьёзный стресс – serious stress
огромный стресс – enormous stress (more emotional)

If you want the most typical, natural phrase, сильный стресс is the best choice.

Why is it на работе and not в работе?

Both на and в can mean at / in, but they are used with different types of nouns and meanings. With работа:

на работе = at work / at one’s workplace / in the work context
This is the normal way to say at work:
- Я сейчас на работе. – I’m at work now.
- У меня проблемы на работе. – I have problems at work.
в работе is possible, but it means in the work / in the process of work, often more abstract:
- ошибка в работе – an error in the work (in how the work was done)
- недостатки в работе – shortcomings in work

So for stress at work (in the workplace / job situation), you must say на работе.

Why is it на работе (работе, not работа)? What case is this?

Работа is in the prepositional case: работе.

The pattern for location is:

на + prepositional (for many places and activities)

Declension:

nominative: работа (work)
prepositional: о работе, на работе (about work, at work)

So:

на работе – at work (location)
в этом месяце – in this month (also prepositional)

Are there other common ways to say the same thing in Russian?

Yes. The original sentence is natural and good, but you might also hear:

В этом месяце я был под сильным стрессом на работе.
Literally: I was under strong stress at work.
В этом месяце я очень нервничал на работе.
I was very nervous at work this month.
В этом месяце у меня были большие переживания на работе.
I had a lot of worries/concerns at work this month.
В этом месяце у меня было много стресса на работе.
I had a lot of stress at work this month.

The original В этом месяце у меня был сильный стресс на работе is straightforward and idiomatic, especially for describing a period with high work-related stress.