You have a number of options:
- More than one object can be made a child of the same Armature
- Join all the objects into a single object and make that a child of the Armature
- Make each part an child of the Armature as an Object, then put an Armature modifier in the stack for each object and specify the same Armature for each
I recommend #3 because it’s perhaps the most flexible. You’ll need to create Vertex Groups in each body part. For rigid parts moved (deformed) by a single bone, this can be the entire mesh as a Vertex Group. Name the VGs according to the bones in the Armature. I don’t recommend using any of the “automatic” weighting options (like Bone Heat) because that distributes the weighting in a way that might not be right for the more rigid robotic look you seem to want.
For the rigid parts, just assign a weight of 1.0 to the entire Vertex Group, named for whatever bone is to control that part. With no other weighting, that bone will move the part as a rigid body. But be careful of the parts intersecting as they move under armature control – you may have to do some re-modeling to account for this.
If you have any parts that should flex (like tubes and such), they can be weight-painted after being given the appropriate Vertex Groups.
Parenting the Armature to a body part “as an Object” is one of the options that pops up when creating the Parent/Child link. Pretty sure you’ll need it for when the entire Armature moves, so the parts will follow.