How do we know Satan entered Judah? We know because scripture says so, specifically. The Bible doesn't say that Peter was possessed. Jesus never told Satan to leave Peter's body. And we aren't told that Satan left Peter's body and fled behind Jesus. It sounds more like Jesus was comparing Peter to Satan because of what Peter said. And Jesus went on to tell Peter, that Peter's mind wasn't on God's interest. That doesn't mean that Peter's mind was possessed. Instead, Jesus said that Peter was thinking like a man. What Jesus said to Peter was an insult, comparing Peter to Satan. Judah's case was completely different.
Matthew 6:21-23 From that time Jesus began to show His disciples that He must go to Jerusalem, and suffer many things from the elders and chief priests and scribes, and be killed, and be raised up on the third day. Peter took Him aside and began to rebuke Him, saying, “God forbid it, Lord! This shall never happen to You.” But He turned and said to Peter, “Get behind Me, Satan! You are a stumbling block to Me; for you are not setting your mind on God’s interests, but man’s.”
God wasn't talking to Satan because Satan wouldn't be setting his mind on God's interest to begin with. That was Peter, the man, not wanting to accept the bad news Christ had just shared with the disciples, and was rebuked by Jesus for it.
We know Eve was influenced by Satan, but it doesn't say she was possessed. We'll have to ask her to clarify for us when we get up there...