"I have my wife."

Translation: Mám svou ženu.

[BossKaiden]

How do you know whether to use "svou" or "moji" and their variants?

[VladaFu]

If the owner is the subject of the sentence use the reflexive forms.

[Mark508579]

It accepted "Já mám moji manželku", but I don't believe it should have, unless the reflexive forms are optional.

[VladaFu]

The reflexive form is normally much better. The non-reflexive forms have their place when you stress you have YOUR wife and not someone else's.

[Mark508579]

Thank you!

[Link-D]

I've seen "svou" and "svoji" used interchangeably when the possessive precedes a feminine singular noun.
(Hledám svoji ženu in a preceding sentence, and Mám svou ženu here.)

Is there a difference? If so, what is it?

[svrsheque]

both are standard. the hard adjective declension (svou) is more formal.