Is it permissible to move into a new residence during the Sefira period, and, if so, may one paint or make other decorative renovations before moving into the new home?
Chacham Ovadia Yosef addresses this question in his work Chazon Ovadia (Laws of Yom Tov, p. 269), and rules that although moving and renovating are forbidden during the nine days before Tisha B'Av, they are allowed during the period of Sefirat Ha'omer. The period of the nine days commemorates numerous different calamities that befell the Jewish people, and therefore the mourning practices observed during the nine days are particularly strict. During the Sefira period, by contrast, we commemorate only a single event – the tragic death of Rabbi Akiva's students – and Halacha therefore imposes more lenient restrictions. Hence, Chacham Ovadia writes, if a new residence becomes available during the Sefira period one may move in immediately, and he is not required to delay his move until after Lag Ba'omer. It is likewise permissible to paint or make whatever renovations one wishes before moving in.
Similarly, he adds, one may conduct a "Chanukat Ha'bayit" celebration for a new home during the period of Sefirat Ha'omer. Words of Torah should be spoken at the celebration so that it assumes the Halachic status of a "Se'udat Mitzva" (a meal involving a Mitzva). Singing is allowed at such a celebration during Sefira, but music should not be played.
Summary: One may move in to a new residence during Sefirat Ha'omer and make any renovations or enhancements he wishes in the residence before moving in. One may conduct a "Chanukat Ha'bayit" celebration for a new home during Sefira without music, provided that words of Torah are spoken at the celebration.