How many Watson-Crick + Hoogsteen triple base pair combinations are there?
You are correct in assuming that the image labeled TAA should be labeled TAT and the second one labeled TAT should be labeled AAT. The image should be removed from the Wiki page until it has been corrected (even so I find it unclear).
Only some of these images show Watson-Crick/Hoogsteen combinations. To answer your question of how many such combinations there are, let us first recall what a Hoogsteen base-pair is. As stated in the first diagram on the Wiki page, this is a non-standard AT or GC base-pair formed by purine rotation about the glycosidic bond and base-flipping. In the diagram I have produced by canabilizing the above I show W-C and Hoogsteen base-pairs with the difference in the glycosidic link shown in yellow overlay. Because the pyrimidines A and C in a W-C base-pair have no groups left to hydrogen-bond, the only way you can theoretically make a W-C/H combination is by ATA and CGC as shown in my diagram. Therefore there are only two such possibilities.





I am not quite sure why you want to know about WC/H combinations, other than to understand the diagram in the article, because they are not particularly important. The author of the diagram shows such combinations because they apparently occur in triple-helices of artificial copolymers, however his diagram also shows some non-Watson-Crick base-pairs, e.g. CGG and CGA (which are not examples of WC/H combinations). The molecule where most Hoogsteen base-pairs are found naturally is RNA, not DNA: e.g. tRNA and ribozymes, in regions which do not have a standard double-helical structure. In these case they can occur in combination with both WC base-pairs and non-WC base-pairs (e.g. the GG illustrated above), so there is nothing special about Hoogsteen base-pairs being combined with WC base-pairs. 


What I would consider important to realize is that in the context of the DNA double-helix WC base-pairs give the most thermodynamically stable structure, but outside this context, especially in RNAs that have protein-like structures, a variety of alternative base-pairs and base-triples are structurally and thermodynamically possible, including but not restricted to Hoogsten base-pairs.