You rightly identify three main theories of learning (i.e., behaviorism, constructivism and cognitivism) and one teaching theory, than one proposed by Dennis Fox.
As teaching and learning and two faces of the same coin (education), every theory of teaching is, to a great extent, also a theory of learning and the other way around. In addition to behaviorism a la F. Skinner, for example, with its emphasis on the role of external contingences (e.g., positive and negative reinforcements, punishment and the like), on students' learning, constructivism a la J. Piaget, for instance, and its idea that the individual is the main responsible for his/her learning (and development), and cognitivism a la R. Sternberg, for example, and its key idea that learning amounts to receiving external inputs, to code them in the mind/brain, to retrieve them, and then to generate an output, we could add to your list Bandura's social learning theory and its key idea that we learn mainly by observing and imitating models, Bandura's social cognitive theory according to which one's learning is mainly a function of six central variables (i.e., attention, retention, motivation, reproduction, self-efficacy, and outcome expectancies), Vygotsky's socio-cultural theory and its essential thesis that we learn under adult guidance or in cooperation with core competent peers, and social constructionism (not constructivism) a la K. Gergen, for instance, according to which any learning is a social and co-construction. Other theories of learning could be also mentioned, as is the case of the so-called new theories of learning, such as those proposed, for example, by H. Feldman, J. P. Leone.
As for theories of teaching, there is a high consensus on the idea that Erikson's theory of socioemotional development with its emphasis on the several levels of such type of development, Gardner's theory of multiple intelligences (e.g., spatial intelligence, intrapersonal intelligence, interpersonal intelligence), and Maslow's theory based on a hierarchy of needs (e.g., basic needs...., self-actualization) are well-known theories that could underlie teachers' teaching.
To sum up, as any theory of learning is, to a great extent, also a theory of teaching and there are several theories of learning, you have on offer several valuable learning theories. It is up to you to choose one or several among them.
I hope I have got your questions and that this helps.
I second the mention of Gardner's Theory of Multiple Intelligences! I have seen great results in student achievement and behavior using MI instruction. Children are empowered by the notion they are "smart" in their own special way.