Is it possible to use an inversion like this:
"Nothing could (can) I do in that situation."
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It is possible and understandable. However I would only expect to see this form in poetry. It certainly is not used in ordinary conversation.
In everyday modern English we would say:
There was nothing I could do in that situation.
From the following Google nGram, you can see that "nothing could I" experienced an upsurge in the mid-1800s and its usage appears to be increasing now. However I believe the latter is because of the re-publishing of old works in modern editions.
Google nGram: nothing could I
Google Books: Recent publications of older works