The different constructions fulfill different functions. Dative and genitive possessor constructions seem to be used for inalienable possession and permanent possession. (No clear difference between the two emerges, except that the dative construction does not require the copula.) The locative human possessor construction is used mainly for temporary alienable possession. The nominative possessor construction seems to be used for nonhuman possession/attribution.
Source: Smith 1974-5: 1659
Source: Smith 1974-5: 1467
Source: Smith 1974-5: 5309
Source: Smith 1974-5: 5479
Source: Smith 1974-5: 0544
Source: Smith 1974-5: 1438
Source: Smith 1974-5: 5256
Source: Smith 1974-5: 5167
Source: Smith 1974-5: 5477
Source: Smith 1974-5: 1950
Source: Smith 1974-5: 4205
Source: Smith 1974-5: 4206
Source: Smith 1974-5: 0542