Context. Variability is a key property of stars on the asymptotic giant branch (AGB). Their pulsation period is related to the luminosity and mass-loss rate (MLR) of the star. Long-period variables (LPVs) and Mira variables are the most prominent of all types of variability of evolved stars. However, the reddest, most obscured AGB stars are too faint in the optical and have eluded large variability surveys. Aims. Our goal is to obtain a sample of LPVs with large MLRs by analysing WISE W1 and W2 light curves (LCs) for about 2000 sources, photometrically selected to include known C-stars with the 11.3 μm silicon carbide dust feature in absorption, and Galactic O-stars with periods longer than 1000 days. Methods. Epoch photometry was retrieved from the AllWISE and NEOWISE database and fitted with a sinus curve. Photometry from other variability surveys was also downloaded and fitted. For a subset of 316 of the reddest stars, spectral energy distributions (SEDs) were constructed, and, together with mid-infrared (MIR) spectra when available, fitted with a dust radiative transfer programme in order to derive MLRs. Results. WISE based LCs and fits to the data are presented for all stars. Periods from the literature and periods from refitting other literature data are presented. The results of the spatial correlation with several (IR) databases is presented. About one-third of the sources are found to be not real, but it appears that these cannot be easily filtered out by using WISE flags. Some are clones of extremely bright sources, and in some cases the LCs show the known pulsation period. Inspired by a recent paper, a number of non-variable OH/IRs are identified. Based on a selection on amplitude, a sample of about 750 (candidate) LPVs is selected of which 145 have periods > 1000 days, many of them being new. For the subset of the stars with the colours of C-rich extremely red objects (EROs) the fitting of the SEDs (and available MIR spectra) separates them into C- and O-rich objects. Interestingly, the fitting of MIR spectra of mass-losing C-stars is shown to be a powerful tracer of interstellar reddening when AV ≳ 2 mag. The number of Galactic EROs appears to be complete up to about 5 kpc and a total dust return rate in the solar neighbourhood for this class is determined. In the LMC 12 additional EROs are identified. Although this represents only about 0.15% of the total known LMC C-star population adding their MLRs increases the previously estimated dust return by 8%. Based on the EROs in the Magellanic Clouds, a bolometric period luminosity is derived. It is pointed out that due to their faintness, EROs and similar O-rich objects are ideal targets for a NIR version of Gaia to obtain distances, observing in the K-band or, even more efficiently, in the L-band.