Good question, tunalover. These terms are used often in solar applications.
Emissivity, or "emissive power" [E(b)], is the rate at which radiant energy is given off by a body per unit area per unit time (often in W/m^2). Emittance (epsilon), on the other hand. is a dimensionless ratio – the ratio E:E(b) – that is, the ratio of the emissivity of a body to the emissivity of a perfectly-emitting and absorbing (theoritical) black body. Thus, emittances are always less than 1.0. Now, to confuse things further, emittances of specific surfaces are often stated AT A CERTAIN, DEFINED TEMPERATURE (sometimes termed "monochromatic wavelength", lambda). This is epsilon (subscript lambda). For instance, fresh snow is said to have a long-wave (thermal band) emittance of 0.82, while epsilon(lambda) for red bricks is 0.92. And black cupric oxide on sheet aluminum has an epsilon(lambda) of only between 0.09-0.21. Of interest to solar engineers is another ratio – the ratio of monochromatic short-wave absorptance to long-wave emittance, for it is desirable to have collector surfaces that absorb a maximum amount of the short-wave solar energy, yet emit relatively little (ie – most of the energy absorbed will be available for use via conduction to the desired application). Incidentally, absorptance (alpha) is itself a ratio of the amount of energy incident on a body to the amount of energy actually absorbed.
Transmittance is a term used in relation to glazing, and it is the fraction of (usually solar) radiation that a particular glazing layer allows through. Transparent surfaces reflect a certain amount of incident radiation, they absorb a certain amount, and they transmit the rest through to the other side. The relative percentages of each phenomenon depend on such variables as the angle of incidence, the chemical make-up of the glazing layer (which itself dictates such values as the index of refraction and the extinction coefficient), and the incoming wavelength. As far as I know, "transmissivity" refers to the same thing, for it is used interchangeably with transmittance in the standard texts.
Hope that helps. Sustainable, Solar, Environmental, and Structural Engineering: Appropriate technologies for a planet in stress.