"Dark" quantities I don't know much about the so-called dark matter, apart from what has been described in popular descriptions of the reasons for it being postulated.
My question is, is there dark momentum, dark charge, dark angular momentum? Also would these fit into the Standard Model (with modifications)? 
 A: "Dark energy" is a label for whatever unknown thing is causing cosmological acceleration. Its effects seem to be the effects you would see from something that had negative pressure, so it would have been equally valid to call it "dark negativepressure" or "dark positiveenergyandnegativepressure." One model of dark energy is a cosmological constant, which has no dynamics of its own, but there are other models such as quintessence that are fields with their own dynamics.
"Dark matter" means matter that doesn't emit or absorb light. The term is conventionally not taken to include dark energy. Although a small amount of dark matter could be baryonic matter (i.e., ordinary matter consisting of neutrons, protons, and electrons) or known types of neutrinos, most of it has to be nonbaryonic, which means that it's made of exotic particles that are currently unknown. This nonbaryonic dark matter could be particles that interact through both gravity and the weak interaction, or it could be stuff like sterile neutrinos that interact only gravitationally. Nonbaryonic dark matter (other than known flavors of neutrinos) is not part of the standard model.
Forming terms like "dark momentum" sounds to me like it may involve a misconception about the relationship of the term "dark energy" to the term "dark matter." Dark energy and dark matter are not closely related. This is sort of like how people think that there is a relationship between the programming languages Java and Javascript, which, despite the similar names, are totally unrelated. In particular, "dark energy" is not a term that refers to the energy possessed by dark matter. 
Because dark matter has mass-energy, it will also have nonzero momentum in almost any frame of reference you choose. But this momentum would not be referred to as "dark momentum."
Dark matter cannot have charge. If it did, it would interact electromagnetically, which contradicts its definition.
Since dark matter can have momentum, it can also have (orbital) angular momentum. Most hypothesized types of dark matter also have intrinsic (spin) angular momentum of 1/2 h-bar, but, e.g., axions would have spin 0.
A: Dark matter is expected to be matter that does not engage in electromagnetic interaction and it's momentum, angular momentum, etc is expected to be exactly the same as that for "normal" matter.
Neutrinos are an example of this kind of stuff, though the three basic flavors are known to be insufficient to make up the bulk of the expected dark matter content.
I'm not going to address dark energy, 'cause little is known about it and I don't even know most of that.
