I understand that according to one of Euler's theorems, any solid object's 3D rotational orientation can be represented by a single 3D vector and an amount, i.e. a 4D vector.
However, is it correct to extend this to momentum? i.e. is it correct that a solid object's rotational momentum can be expressed by a vector? Or are there more complicated factors at play (e.g. wobble, etc.)
Of course it can. Angular momentum (the rotational analog to linear momentum) can be expressed as an axial vector (sometimes called pseudovector), which means a quantity that is similar to a regular vector, except for the fact that it changes sign under improper rotations (such as reflections). I suppose you're refering by "wobble" to nutation, i. e., a small oscillation on the axis of rotation of a spinning object, such as a top.
This is related to the presence of an external torque, which produces an angular acceleration, then a change on angular momentum:
$$\tau=\frac{dL}{dt}$$
For a more detailed explanation of the mechanism behind the nutation effect, see the answers to this question.
