Why are there multiple sequences for the same segment for an individual "strain" of influenza?
It looks to me that the website you're looking at is mostly taking publicly available data from Genebank (the NCBI repository for sequence data) an collects it to form an overview.

For your question this means that there are 4 available sequence datasets for the A/Michigan/45/2015 influenza strain - they are likely very similar but based on the reported segment length not quite identical. 


  Or is it that they are including both positive and negative sense of the virus?


If you mean the positive and negative strand of the DNA, then no - since the sequence of these two is always complementary the Genebank repositories only stores the forward sequence.

You can also see that the 4 different datasets have similar Acession numbers:
KY117020 - 27 (Passage M1/C3)
KU509700 - 07 (Passage E1)
KU933490 - 07 (Passage E3)
KY090607 - 14 (Passage M1/IR)  

You can look up more details for these accessions on the genebank website: 


It seems that all 4 datasets came from the same publication  
... which apparently was never published (so it's not available online), but it might be part of some WHO program?  
The main difference of the 4 datasets I can find is the passage of the strain. I'm no virologist, so I'm not quite sure what it means, but in cell biology passage describes the time a certain cell line has been in (in vitro) culture.