Context. Radio halos are elusive sources located at the center of merging galaxy clusters. To date, only about 40 radio halos are known, thus the discovery of new halos provides important insights into this class of sources. Aims. To improve the quality of the statistics of radio halos, we investigate the radio continuum emission of a sample of galaxy clusters. Methods. We analyzed archival Very Large Array observations at 1.4 GHz, with a resolution of 1 . These observations were complemented by X-ray, optical, and higher-resolution radio data, leading to the detection of a new radio halo in the central region of A800 and A1550. We discovered a radio relic in the periphery of A910, and finally revealed both a halo and a relic in CL1446+26. Results. The clusters hosting these new halos show an offset between the radio and the X-ray peak. By analyzing this offset statistically, we find that radio halos can be quite asymmetric with respect to the X-ray gas distribution, with an average radio-X-ray displacement of about 180 kpc. When the offsets are normalized by the halo size, there is a tendency for smaller halos to have larger displacements.