Esposo (spouse) is a bit old-fashioned, I rarely see people using it. Marido (husband) is the standard one. Homem (man) is a lot more informal and it sounds a bit possessive, so I only see it being commonly used when picking up a fight, e.g.: "Não acredito que essa vadia deu em cima do meu homem!" "I can't believe that ❤❤❤❤❤ hit on my man!".
For women, both esposa (spouse) and mulher (wife/woman) are commonly used.