Terminology question: the scope of an allele in an organism
If I were discussing a SNP of FOO that gives rise to foo in a tumor
  cell of an organism, I wouldn't say that the organism has foo, but I
  might say that the tumor has it.


You can call it a somatic mutation. See this paper. They report such mutations in cancer. 

You can use the term like this:


  Carcinoma tissue had a somatic mutation in XYZ oncogene, thereby making it constitutively active.





  If I were discussing a chimeric or mosaic organism in which some
  fraction of the chimera had foo and the other fraction had FOO


In this case you can say:


  The organism is chimeric for gene-X, expressing variants X1 and X2


From this article:


  Effects of AngII-Infusion Into LDL Receptor−/− Mice That Were Chimeric
  for AT1a Receptors