The pulsed-laser-induced transient thermoelectric effect (TTE) and the static transport properties (resistivity, Hall coefficient, magnetoresistance, and thermopower) of a quasi-two-dimensional \ensuremath{\eta}-${\mathrm{Mo}}_{4}$${\mathrm{O}}_{11}$ crystal have been measured over the time range 50 ns--2 ms and temperature range 4.2--300 K. The observed TTE voltages decay exponentially with time, showing relaxation processes with multiple relaxation times ${\mathrm{\ensuremath{\tau}}}_{\mathit{i}}$ (i=1--5) for thermal diffusions of photogenerated carriers (electrons and holes), from which we can evaluate the corresponding carrier mobilities ${\mathrm{\ensuremath{\mu}}}_{\mathit{i}}$. The temperature dependences of both dynamic and static transport quantities show anomalies around the characteristic temperatures ${\mathit{T}}_{\mathit{c}1}$=105 K and ${\mathit{T}}_{\mathit{c}2}$=35 K; ${\mathit{T}}_{\mathit{c}1}$ is the well-known charge-density-wave (CDW) transition temperature, but for the latter no definitive x-ray evidence for a CDW transition is reported. However, using our dynamic data and the existing two-dimensional tight-binding model, together with our proposed nesting model of the Fermi surfaces and the CDW-related modifications of the electron and hole bands at ${\mathit{T}}_{\mathit{c}1}$ and ${\mathit{T}}_{\mathit{c}2}$, we have self-consistently calculated the temperature dependence of the dc transport quantities, in satisfactory agreement with the experiments.