How to manage two tables in SQL Server
Try this:

select osd.UserId, osd.OfferId, ou.OfferName
  from dbo.offersentdetail as osd
    inner join (
      select OfferId = Offer1Id, OfferName, OfferExpiryDate
        from dbo.[Offer1] 
      union all 
      select OfferId = Offer2Id, OfferName, OfferExpiryDate
        from dbo.[Offer2] 
        ) as ou
    on osd.OfferId = ou.OfferId