What restrictions exist for publishing on strong encryption in USA? In the past, there were export and other restrictions on publishing information, source code or otherwise making new strong cryptographic items available without prior government approvals.

There are many conflicting regulations, laws, constitutional freedoms like freedom of speech and various legal precedents that make this area confusing; ITAR, EAR, etc.

So my specific questions are, are there still legal or regulatory restrictions for U.S. citizens that prohibit our ability to publish papers and articles about strong encryption techniques, improving existing techniques or introducing new cryptographic methods? 

How about publishing source code accompanying such papers which are made publicly available? Is that still considered “exporting” that requires approval?

Edit1:
That’s helpful guidance on software/hardware items.
What about simply publishing research papers about improving and supplementing existing algorithms like AES, ChaCha, etc. without actually shipping anything other than a published paper?
My experience is from my time working in the State of Georgia, and firstly, how true that you want to stick to this depends on your funding source, and your end goals.  

For software, the truth is probably nothing needs to be done in a practical sense due to Bernstein v. USA, but it's legally more complicated, and the details are here.
By the letter of the law: If your keys are greater than 64-bits, each time the cryptographic functionality of the source code is updated or modified you have to notify NSA and the U.S. Department of Commerce Bureau of Industry and Security (BIS).  If there are changes, you will need the specifics to notify BIS and NSA.  I also explicitly keep embargoed countries and people from accessing the files because I only distribute them on request.  This means that you can do whatever, and then publish the source code if you notify BIS.  I also send them updates every 3 months to say "nothing has changed" because if not, they ask.

For hardware, it's much more complicated because it is much more inconvenient.  I cannot fab anything without the proper forms in place, and the fabs enforce this as well.  I need a product ECCN.  Another annoyance is that I always end up making "hardware for export" for conferences.  For example, I have a power attack for SIMON128/256, but I've only shown the SIMON32/64 attack publicly because there's no way to guarantee who's in the audience. 

The biggest issue of why to care is the funding source.  If you get USA money, you want them to feel like you are playing by their rules.  I've put up with the bureaucracy so I've been able to get repeat funding for semiconductors, and those aren't cheap.