The purpose of the present paper is to clarify, as far as it is possible, the overall picture of experimental results in the field of non-conventional phenomena in nuclear matter published in the scientific literature, accumulated in the past few decades and still missing a widely accepted interpretation. Completeness of the collection of the experiments is not among the aims of the effort; the focus is on adopting a more comprehensive and integral approach through the analysis of the different experimental layouts and different results, searching for common features and analogous factual outcomes in order to obtain a consistent reading of many experimental evidences that appear, so far, to lack a classification in a logic catalogue, which might be compared to a building rather than a collection of single stones. Particular attention is put on the issue of reproducibility of experiments and on the reasons why such a limitation is a frequent characteristic of many experimental activities reported in published papers. This approach is innovative as compared with those already available in the scientific literature. In a synoptical table, a comprehensive classification is given of the twenty experiments examined in terms of types of evidences that are ascertained by the experimenters in their published papers but are “unexpected” according to well-established physical theories. Examples of such unexpected evidences (named also non-conventional or weird) evidences are: excess heat generation, isotope production, reduction of radioactivity levels, and production of neutrons or alpha particles. These evidences are classified taking into account both the material where the evidence takes place (solutions, metals, rocks and artificial materials) and the stimulation techniques (supply of electric voltage, irradiation by photons, mechanical pressure) used to generate the evidences (which do not appear in the absence of such stimuli at an appropriate intensity). Also, in our paper, “identity cards” are provided for each experiment examined, including details that emerged during the experiment and were reported in each respective paper, that sometimes are not given adequate consideration either by the author of the experiment or in other review papers. The analysis of the details provides suggestions (also referred to as clues in this papers) used to formulate the content of the second part of each identity card, where inferences deduced from facts are outlined in view of presenting tentative interpretation at the microscopic level. This is done by concentrating attention on the clues repeated in different experiments in order to yield possible explanations of the “unexpected” evidences. The main outcome of such analysis is that, in all examined cases, a common “operation” can be identified: the stimulation techniques mentioned above can be interpreted as a sort of compression producing a ramp of energy densification (with reference to volumes in space or time coordinates). Here we use the term “compression” to indicate an operation activated by the experimenter; as such, it is objective. We consider energy densification an inference of possible consequences of the operation on the status of the system. Five types of densifications were identified. This reading in terms of energy densification is in accordance with the predictions of the Deformed Space Time theory, reported in the scientific literature, in the context of a generalization of the Einstein relativity theory, according to which the existence of energy thresholds is found to separate, for each interaction, the flat metric part from the deformed metric part and the appearance of new microscopic effects as a consequence of trespassing such thresholds. The phenomena occurring in the deformed part of the interaction metric are governed by the energy density in the space-time (volume and time interval). This energy density is computed from the threshold energies and is peculiar to the phenomenology under consideration. As a conclusion, it is suggested that the revealed qualified information, homogenized and elaborated on, might help in repeating, with proper adjustments and adequate additional instrumentation, some key experiments, in order to ensure systematic reproducibility, which is a prerequisite for interpretations and explanations to be sound and credible, as well in deriving from such an effort, indications for new experiments. It is uncomfortable that, after thirty years, there are still pending questions to which the most acknowledged physical theories are not capable of giving an answer. Even a definitive demonstration that all these experiments have decisive faults would be preferable than leaving the issue unaddressed. Major research agencies, for instance in the USA and in Europe, are moving in this direction.