Psalm 81 - Overcomer - Hear Him and Walk in His Ways
This psalm is a miniature of the long ballad, The Song of Moses, in Deuteronomy 32.  God Himself speaks, telling Israel to hear Him and to walk in His ways and what the results and consequences would be.
v1 - See Psalm 8, v1 for comments about "upon the winepresses".
If not for the first 2 verses, I would not know that this was a joyful song.  The combination of joy and rebuking is wonderful.
v2 - Don't be reserved in singing this song.
v3 - This tells me that this psalm should be sung monthly.
v4- Lit. "Because for Israel this is a statute."
This song is to be sung at the feasts of Israel as a remembrance. This is like the Lord's Table which the Lord commanded us to keep as a joyful remembrance of Him and His death (Luke 22:19; 1Cor 11:23-26.)

Another brother and I wrote a song about the Lord's Table here.
v5 -  "Joseph" is spelled uniquely here. It actually is "Jehoseph", a combination of the names "Joseph" and "Jehovah". This is the only occurrence of this spelling. This shows the oneness of God with Joseph and vice-versa.

God went forth over the land of Egypt at the time of the exodus when the children of Israel were slaves there.
"I heard a language I knew not" shows how Israel felt as a stranger in Egypt. God felt His people's predicament.
v6 - As Christians, we have been grafted into Israel, and Israel's experiences are our experiences also (1Cor 10:1).

"We should never forget our deliverance from a more intolerable servitude; but commemorate it - specially in the Lord's Supper." - F. B. Meyer
v7 - This is so sweet. (Ps 55:22)

The Lord still proves us at the waters of strife. We will have strife in our lives, and the Lord proves our hearts by it. (Phil 1:27)
v8 - Lit. - if you would hearken unto Me
This plea of God is similar to Psalm 50 (Ps 50:7), also by Asaph. It is also the plea of the epistle to the Hebrews chapters 3-4.
v10 - Ask the Lord difficult things according to His will.
Nothing is too difficult for Him. The Lord wants us to open our mouths wide to Him, not just a little bit. (John 14:12 ...)
The Lord's filling our mouth is answering our prayer which also satisfies us, making us full of joy (v16).

When George Mueller was first praying about whether he should start an orphanage, this verse spoke to him:
"On Dec 5th [1836], however, the subject of my prayer all at once became different. I was reading Psalm 81, and was particularly struck, more than at any time before, with verse 10. I thought a few moments about these words, and then was led to apply them to the case of the Orphan-House. It struck me that I had never asked the Lord for anything concerning it, except to know His will, respecting its being established or not; and I then fell on my knees and opened my mouth wide, asking Him for much. I asked in submission to His will, and without fixing a time when He should answer my petition. I prayed that He would give me a house, i.e., either as a loan, or that someone might be led to pay the rent for one, or that one might be given permanently for this object; further, I asked Him for 1000 pounds; and likewise for suitable individuals to take care of the children. Besides this, I have been since led to ask the Lord to put into the hearts of His people to send me articles of furniture for the house, and some clothes for the children. When I was asking the petition, I was fully aware what I was doing, i.e., that I was asking for something which I had no natural prospect of obtaining from the brethren whom I know, but which was not too much for the Lord to grant."
v11 - When we pray we also need to hear the Lord's speaking to us often through His word (Heb 3:7-8 ...)
v12 - "gave them up" is literally "sent them".
v13 - lit. "Oh that My people would hear Me"
v14 - lit. "And upon their adversaries I would return My hand"
I followed Young's Literal Translation of this verse. Most translate "Like a little thing" as "soon", but there is the prefix "like" attached to it. Leupold translates it as "easily".
v15 -  People who hate the Lord pretending obedience to Him are hypocritical worshippers of the Lord. When Jesus, as God in the flesh, visited His people Israel, their religious leadership showed their hate for God by despising Jesus (Zec 11:8). Asaph, the author of this psalm, prophesies about them in his first psalm, Ps 50:16-22. and in the very next psalm, Psalm 82, Asaph prophecies about their encounter with the Lord Jesus in John 10.

This verse says literally: Haters of the LORD  will feign obedience unto Him, and their time became to the age (or forever).

Questions: Who does "their" refer to: Haters of the LORD or Israel?  It should refer to 'haters of the LORD" since that is what immediately precedes it. For Israel, the 3rd person singular pronoun is used in the following verse.

What does it mean that "their time became to the age"? I think it means that rejection of the Messiah would prevail in Israel until the end of this age. It also means that Israel's enemies and haters of the Lord would prevail until the end of the age.
When Israel's hypocritical God-hating leaders killed their Messiah, Israel's time was delayed until the end of the age, and Israel's rejection of their Messiah became until the end of the age. The interval between the crucifixion of the Messiah and when God visits Israel again is called "the times of the Gentiles" (Luke 21:24).

This verse is the ultimate result of Israel not listening to God nor walking in His ways.
v16 - This concluding verse of blessing is from the long ballad, "The Song of Moses", which is a rebuking song for Israel to understand why God would forsake them in the future until the last days, so they could turn back after it happened.  This ballad of the Song of Moses informs my interpretation of the previous verse.

"Honey out of the rock" denotes the sweet, strong and dependable enjoyment of God Himself.  

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