Assuming 030 level is one Publication you should be able to copy/cut and paste the items. Copy/cut and paste will keep all component linking in place, so should be pretty painless.
n.b. If you copy a parent component e.g.
Component A, with Component Links
and rename it to be
Component B, the it will still link to Component Links
3. These will need to be updated separately if required.
In your case, take for example a Component
A with several Multimedia Components in it. Within the same publication you could move the Component
A and/or any or all of the images without breaking the links between them. Simply copy/cut and paste to a preferred location.
Copy/Cut and paste can be used on all items (Components, Folders and Pages etc..) as long as it is within the same publication.
If you are looking to move items across publications, as Nick says, you will need to recreate them. Depending how many items you are looking to move you can either do this manually, or create a Core Service script to move them programatically. Careful consideration should be made to maintain cross-linking and pages with either approach.
Another approach I have used in the past, but really depends on circumstances is to use Content Porter to move items across publications. In effect tricking Content Porter to move the items across publication using re-naming. Again, this should be done with caution and considering all implications.
These few blog posts and other SE question cover the approaches at a high level
Using Core service to copy items to different publications