How viscous is the Earth's mantle? I'm posting here to get some more expert information based on this question.

If the Earth were to stop rotating, removing the centrifugal force causing the equatorial bulge, how long would it take for the mantle and crust to return to hydrostatic equilibrium?  That is, immediatly, thousands of years, or millions of years?

Never mind that changing the rotation in reality would involve forces and timescales that would not really provide this condition. if matter were arranged in such a shape, how long (orders of magnitude) would it take to settle?
The mantle viscosity is likely to be non-linear, e.g., it could be as low as $10^{18} \textrm{Pa}\cdot\rm s$ (over shorter time scales) or as high as $10^{21} \textrm{Pa}\cdot\rm s$ (over longer time scales). In any case the values reported in the literature are somewhere between $10^{18}-10^{21} \textrm{Pa}\cdot\rm s$ and these are based on studies from earthquakes, glacial rebound etc. So you can calculate the relaxation time(s) using these two end member values. 

E.g., if you assume the average i.e., $10^{19.5} \textrm{Pa}\cdot\rm s$ then we get a relaxation time of $10^{19.5}/150\cdot10^9$ (viscosity/mu) which is $2.1082\cdot10^8$ seconds or ~$6.6$ years.