YES, Old Testament scriptures can and should be used in Sunday sermons AND in all teaching situations.

I Peter 1:10 to 12 says, “As to this salvation, the prophets who prophesied of the grace that would come to you made careful search and inquiry, seeking to know what person or time the Spirit of Christ within them was indicating as He predicted the sufferings of Christ and the glories to follow.  It was revealed to them that they were not serving themselves, but you, in these things which now have been announced to you through those who preached the gospel to you by the Holy Spirit sent from heaven—things into which angels long to look.”

Later in I Peter 3:21 & 22, Peter writes, “And corresponding to that, baptism now saves you—not the removal of dirt from the flesh, but an appeal to God for a good conscience—through the resurrection of Jesus Christ, who is at the right hand of God, having gone into heaven, after angels and authorities and powers had been subjected to Him.”

Notice the first phrase, “And corresponding to that.”  What, exactly, is “that?”  The answer is found in last part of verse 20, “when the patience of God kept waiting in the days of Noah, during the construction of the ark, in which a few, that is, eight persons, were brought safely through the water.”

Without the Old Testament scriptures in Genesis 6:1 to 8:19 we would have NO idea to what Peter was referring in this I Peter 3:20 to 22.

In  I Timothy 3:16 and 17 Paul says, “All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; that the man of God may be adequate, equipped for every good work.”

Notice, Paul writes, “ALL scripture.”

Also, in Romans 15:4 after quoting from Psalms 69:9 in verse 3, Paul writes, “For whatever was written in earlier times was written for our instruction, that through perseverance and the encouragement of the Scriptures we might have hope.”

Finally, I will refer you to I Corinthians 9:9 & 10, and I Corinthians 10:11.

The apostles made frequent use of the Old Testament, as did Jesus during his ministry here on earth (Matthew 4:10 and 22:37) which is all the authority we need to use the Old Testament whenever and wherever we need.