Can police officers legally come into your home if nobody is there and didn't have permission from the owner?

How would you know if they were if nobody was there? There has to be a reason for asking this. If they have a warrant the owner can't refuse them and neither could you.

If they believe and have cause to believe that a crime is in process or if they have a warrant to search or an arrest warrant, they may go in.

OK I understant that, but no crime was being committed and they DID NOT show me a warrant,

Did they BELIEVE or SUSPECT a crime was being committed? Maybe more details from you will help us answer.

How would you know if they were if nobody was there? There has to be a reason for asking this. If they have a warrant the owner can't refuse them and neither could you.

Cause I was on my street where I could see my house, the first two officers was tying to divert me from my home, as I was walking back to my home and came to the driveway about to walk on my porch there was to undercover officers coming out my home and the DID NOT show me a warrant

Did they BELIEVE or SUSPECT a crime was being committed? Maybe more details from you will help us answer.

No they were looking for my husband and They already knew he was not in there cause they asked me how he got to work that day,

They are not required to "show" you a warrant, in fact often they don't have one in their hand ( like the TV shows) there is merely one issued and they have knowledge of it though their computer systems. At times they may have one with them, but don't show it unless asked for it, and then may be rude about it.

And sorry, they expect you to lie, and no the don't know he is not there till they search. So it appears they had a warrant to arrest your husband, so yes they can come in a listed residence of him.

Also if he is on probation or parole, and they are looking for him, or just want to search where he lives, they can come in without a warrant with permission of the probation office

This may have been legal, it may not have been.
Not enough information yet.
Was the door open, were they there to arrest him, or did he violate parole, or did they just want just question him?
Two uniforms and two undercovers is a lot for just questions.