Where can I find info or techniques on calculating the influence of a duct on the thrust and efficiency of a propeller?
There is info on power computations for ducted propellers in J. Gordon Leishman, Principles of Helicopter Aerodynamics. The beneficial contribution of the duct can be found in section 6.10.1 Fan-in-fin Design, and in section 3.3.10 Prandtl's Tip-Loss Function. In short:




If the duct is designed to prevent wake contraction, extra thrust is generated and less power is required to drive the propeller. The effects are computed with momentum theory, which is a simplification. For thrust T and power P, with $T_D$ and $P_D$ = ducted, $T_U$ and $P_U$ = unducted, $a_w$ = ratio of outlet/propeller area.:


$$\frac{T_D}{T_U} = \frac{1}{2a_w} \tag{1}$$
$$\frac{P_D}{P_U} = \frac{1}{\sqrt{2a_w}} \tag{2}$$


Tip loss. The duct prevents circulation loss at the tip if the clearance between tip and duct is small enough. Prandtl has been working on this in 1919 using momentum theory, an example for an untwisted blade is depicted below.


 

There is also this masters thesis, with measurements of small ducted rotors with low tip speeds.