Are there still journals who only publish their papers in the paper form? As far as I can say, for the papers published nowadays, there is usually a possibility to get an electronic version of the paper. (Often it requires payment or institutional subscription, but many publishers offer the papers free of charge for older issues.) 

Are there still journals, which do not offer possibility to get electronic version of the paper online and use paper version as the only way of distribution of their journal? If yes, is it the case only for small publishers? Are there differences between various disciplines? (I have experience mostly with mathematics.)
Yes. But they are more or less irrelevant at this point. Very, very few people will bother to read them.

One journal in my own field was strictly print until a couple of years ago. They are finally included in one database, but with a five year embargo (meaning only very old articles are available electronically). Another newer journal with a similar target audience is completely open access. Obviously, the open-access journal is getting cited more, the established paper-only one less and less.

In my opinion, the aversion to making a journal available electronically is based on old-fashioned technophobia. There is no serious rationale for it. Yes, they could get more money from actual subscriptions if libraries and/or individuals were willing to pay for them, but that's simply no longer a viable model.