Are there certain days of the week on which one should or should not move?
One should not move homes on Monday (including Sunday night) or Wednesday (including Tuesday night).
It most auspicious and preferable to move on Tuesday (including Monday night). If the entire move cannot be done on Tuesday, at least move the first items on that day.
[This time of year (the three weeks), one should bear in mind that it is preferable to delay moving until Elul, or at least until the 15th of Av.]
Also any other Halachos that are related to moving?
It is customary to bring bread and salt into the home among the first items, as well as Seforim (including a Siddur and Chitas) and Tzedokoh Pushka.
Soon after moving into the new home, one should conduct a Chanukas Habayis gathering with food and drink, including words of Torah and Chassidus (such as reviewing some points from Maamarim on the Possuk of Mizmor Shir Chanukas Habays). It is also appropriate to say words of Tefillah, as well as words of praise and thanks to Hashem.
It is also customary to arrange a gathering of young children to recite Alef Beis and/or Pesukim etc., and to distribute sweets to them.
Of course, make sure to check that you have Mezuzos for all entrances that require one, and affix them at the correct times.
A partial list of sources:
Sefer Minhagim page 81,
Igros Kodeh volume 14 page 379, volume 15 page 3909,
Tzemach Tzedek CH”M Miluim §29,
Sichas Purim 5712,
Sefer Hasichos 5748 volume 2 page 642.