Is there any strong enough pen-and-paper or mind cipher? Some ciphers are talked about at “Is there a secure cryptosystem that can be performed mentally?”, but (at the time of writing) I don't see an answer. 

Are they strong enough, or are non-computer ciphers more or less just a toy and one should abandon using them for practical purposes?
"Strong enough" is a broad term. Some things that you need to keep in mind are entropy size and cryptanalysis. "Strong ciphers" are ciphers that have shown to have enough entropy to withstand practical attacks over time from public scrutiny.

With that said, the Solitaire cipher has a keyspace of roughly 238 bits. By comparison, many SSL keys on the internet are 128 bit AES. Distributed.net is currently working on cracking a 72 bit key, via brute force, at a pace of about 300 billion keys per second, and they have well over 100 years before the keyspace is fully exhausted.

So, for the Solitaire cipher to not be taken seriously, it needs to show practical weaknesses outside of brute force searching. So far, the only weakness that has been demonstrated is that the output has a bias of 22.5:1 rather than 26:1 pure random output would have. This isn't severe enough to mount a practical attack.

As such, until other attacks are made known, to Solitaire cipher is a "strong" hand cipher, that doesn't have NSA influence, can be used without incriminating tools and is easy to learn and remember.