On sociology
It's not like the power people are studying one area while the economic people are studying another. They're all looking at society as a whole, but from different premises. That's why it's incoherent: all 4 will look at the same phenomenon and confidently describe it in mutually incompatible ways.
1 Hard core interactionism/social constructionism: Social reality is defined mainly by how it's enacted in specific situations and these vary quite a bit. Moreover, interactions aren't necessarily reducible to the broader social order. The more radical elements of this tradition run into post-modernism - there is no coherent social reality because it's created differently in different contexts (i.e., no coherent self). You see it also pop up in the strong sociology of knowledge (construction of ideas may have little to do with "reality").
2 Critical social theory: The basis of social reality is power. This can be defined in economic terms (Marx), race (DuBois), or gender (feminists). Or it can be generically defined (Bourdieu). Most of social life boils down to struggle over the stuff that gives your power, or resisting the power.
3 Values, institutions, and relations: This is the broad trend stemming from Weber and Durkheim. The basic elements of VI&R are that human communities have values, which are translated into order via rules, organizations, and institutions. This basic set up motivates everyone from Parsons, to Selznick, to Sumner, to Luhmann, to the world polity crowd. The flavors may be different, but they're all about the push and pull between values and structure.
4 Resources and Action: This strand represents what might be called the "economic view" on things. Psychology and values are strongly de-emphasized and you just work on strategic action. The old version was called "social exchange." Now we call it rational choice. But the R&A tent is big enough to catch some other types of sociology. Organizational ecology - psychology thin and focusing on competition - fits here as well. So might lightly theoretical stratification research.