How can Hindi Oblique case be mapped into Slavic cases of languages such as Polish or Russian? My intuition is that Oblique case stands for all the Polish cases, except the nominative. That is, for example, where Polish uses dative, accusative, instrumental, vocative, instrumental, dative, locative Hindi would use oblique case?
Your understanding is quite decent.
The oblique case in Hindi is used before postpositions which correspond to the case suffix in more richly inflected languages. Since the nominative requires no postposition, there is correspondence with the Hindi nominative and that of other languages.
A study of Marathi, a related Indian language, would help. It is traditionally described as having cases. However, for the most part, the case suffixes are added to a form of the noun or pronoun known as the sāmānya rūpa (सामान्य रूप), which is usually standard for all cases except for the nominative. The Hindi oblique evolved in parallel with the Marathi sāmānya rūpa.