He is in his room 'with a book'/'with a table'

(1) He is in his room with a book.

(2) He is in his room with a table.

Why does (2) sound strange even if it has the same grammatical structure of (1), which works perfectly.

Because when someone is in their room with a book, we can fill in what they are doing that makes the book relevant; viz, they are reading it.

When we are told someone is in their room with a table, there is nothing grammatically incorrect, or even tricky with the preposition (and they can be tricky), it's just a strange thing to say. Why are they with a table? Why would I care? Why bother to tell me?

Now the actual sentence "He is in his room with a book." doesn't explicitly say that "he" is reading that book. Perhaps he is dancing around a copy of Hamlet and invoking the shade of Shakespeare. Perhaps he is using the book for target practice. We're not told that he is not doing these things, but given that there is a particular common activity one might do when alone in a room with a book, we'll fill that in absent any reason not to.

There is not a particular common activity one might do when alone in a room with a table, so we can't fill in the information necessary to understand why we're being told about this table.

This strangeness is different to the strangeness of "He elephant artichoke rubber the minkimoo", which is just nonsense or even "Colourless green ideas sleep furiously" (known words in grammatically correct position conveying no meaning) or "Twas brillig, and the slithy toves. Did gyre and gimble in the wabe" (invented words whose purpose we guess at from their position).

It's the strangeness of a statement that is strange to convey. As such it could be used deliberately:

He is in his room with a table. I don't care who used to own it or how old it is, anyone who spends 2 hours just looking at their furniture should not be allowed to buy antiques.

Here we deliberately baffle a bit, because we go on to express that we think his behaviour is strange, and that moment of bafflement helps convey that opinion. More often, such bafflement will make us think the writer is strange, not their subject.

The niceties of prepositional usage are bewildering.

We'd consider it natural to use 'with' to indicate 'alongside [an equal or near-equal]':

He's in his room with his son / the butler / his dog / ??his goldfish.

We'd consider it natural to use 'with' to indicate 'and has the following portable leisure item/s':

He's in his room with a brandy / a book / his collection of foreign coins / his oboe / ??his piano / ??his pressure cooker.

There's an intimacy involved so far.

Obviously, 'He's in the room with the piano' and 'He's doing some daft experiment - he's in his room with the pressure cooker' don't connote intimacy.

So 'He's in his room with a table' would only work when specifying proximity rather than giving an intimacy / cosiness relationship: