Learn Portuguese (Portugal): É o quarto mais nojento que eu conheça; não têm nenhuma higiene. - It is the most disgusting room that I know of; they do not have any hygiene.

Because it follows a superlative (o quarto mais nojento). Using the subjunctive in this relative clause adds a layer of subjectivity, translating to "that I know of" or "that I have ever experienced," rather than stating an absolute, objective fact.

If we used the indicative "conheço" instead, how would the meaning change?

Using conheço is grammatically possible but sounds more literal and factual, as if you are simply identifying a room you are familiar with. The subjunctive conheça is much more natural here because it emphasizes that this is your subjective opinion based on your personal limits of experience.

The first half is about a singular room, but the second half uses the plural verb "têm". Who is the subject here?

The plural têm implicitly refers to the people who own or manage the room. Just like in English, Portuguese frequently uses the third-person plural without an explicit subject to mean "they" in a general sense, such as the management or staff.

Is the adjective "nojento" related to the common exclamation "Que nojo!"?

Exactly. It is the adjective form of the noun nojo, which means disgust or revulsion. While Que nojo! means "How disgusting!", nojento is the perfect word to describe something that causes that feeling.