What are the sign conventions for moments in a 3-D structure?

The sign conventions are as follows:

Axial (FX) : Positive = Along local X axis, Negative = Opposite to local X
axis
Shear-Y (FY) : Positive = Along local Y axis, Negative = Opposite to local Y
axis
Shear-Z (FZ) : Positive = Along local Z axis, Negative = Opposite to local Z
axis

Torsion (MX) : Positive = Along local X axis, Negative = Opposite to local X
axis
Moment-Y (MY) : Positive = Along local Y axis, Negative = Opposite to local
Y axis
Moment-Z (MZ) : Positive = Along local Z axis, Negative = Opposite to local
Z axis

For axial forces,

Positive at the start node indicates compression at the start node.
Positive at the end node indicates tension at the end node.

Negative at the start node indicates tension at the start node.
Negative at the end node indicates compression at the end node.