If a child has blood type O, it means both his alleles are recessive (since A and B are dominant over O); one of them he gets from their mother, and the other one from their father. That means that the father must have at least one recessive allele that he transfers to the offspring; so the possibilities of the father's genotype are OO, AO or BO.
As for the Rh inheritance, it is pretty much the same: positive allele is dominant over negative. So in order for somebody's phenotype to be expressed as positive, the child only needs one positive allele. We only know that the mother is Rh+, so likewise her genotype is either Pos/Pos or Pos/Neg. Therefore she either donates her Pos allele to the offspring - in this case, it absolutely does not matter what the child receives from his father; or she transfers her Neg - here, the child has to get a Pos from his father, which leaves the father with possible genotypes Pos/Pos or Pos/Neg.
Some pretty accurate additional info at: