Should marriage be prioritized over Hajj, or Hajj over marriage, if a Muslim possesses sufficient funds for only one of them, while fearing falling into sin if he does not marry, and desiring to build two homes before marriage, knowing that Hajj is an obligation?

If you fear falling into the forbidden and have sufficient money to marry, then marry immediately, even if that delays Hajj for years. Do not postpone marriage for the sake of building houses. However, if you are able to control yourself and the conditions for Hajj becoming obligatory are met, then prioritize Hajj because it is an immediate obligation, and marriage is not obligatory for someone who does not fear falling into the forbidden. This is supported by the hadith (definition), "Whoever among you can afford to marry, let him marry," and the hadith, "Whoever intends to perform Hajj, let him hasten to do so."