What was fulfilled and is no longer binding in Old Testament

The  case against the Law by the Apostles

We ought to be careful not to blindly jump to conclusion when the Apostles are discoursing about the inability of the Law to bring about the perfection of the sacrifice of Jesus or that the Law was a shadow of things to come (Colossians 2:16-17, Romans 14:14-17; etc). Remember what Jesus declared about the same Law:

Matthew 5:17-19 EMTV

(17)  "Do not think that I came to abolish the Law or the Prophets. I did not come to abolish, but to fulfill.

(18)  For assuredly I say to you, until heaven and earth may pass away, one iota or one tittle shall by no means pass away from the law until all things are fulfilled.

(19)  Whoever therefore shall break one of the least of these commandments, and shall teach men thus, will be called least in the kingdom of heaven; but whoever does them and teaches them, he shall be called great in the kingdom of heaven.

In food or in drink

Romans

The Apostle Paul is not contradicting Jesus's position in any way. We have to consider what aspect of the immutable Law the Apostle is discussing. For example, Paul made that statement

Romans 14:2 EMTV

(2)  One indeed believes that he may eat all things, but another, being weak, eats [only] vegetables.

Is Paul talking about food considered unclean in Romans 14:2? He continued to say in the chapter"

It is good neither to eat meat nor drink wine nor [to do anything] by which your brother stumbles or is offended or becomes weak.  (Romans 14:21 EMTV)

It is clear that Paul is discussing eating flesh or herbs (vegetables) with no unclean flesh alluded to and the drinking of wine. Paul even advised Timothy to use some wine for his stomach issues ().

To the Corinthians, Paul addressed the doctrinal problem of eating food sacrificed to idols. He concluded again by talking about meat for the act of eating. He says we should not eat meat if the eating would cause our brother to stumble. Again, nothing about eating unclean meat.

Corinthians

1 Corinthians 8:11-13 EMTV

(11)  And because of your knowledge shall the weak brother perish, for the sake of whom Christ died?

(12)  But when you thus sin against the brothers, and wound their weak conscience, you sin against Christ.

(13)  Wherefore, if food causes my brother to stumble, I will by no means eat meat, lest I cause my brother to stumble.

We do read the translation that uses the word "unclean" in Romans 14:14,

Romans 14:14 EMTV

(14)  I know and am convinced in the Lord Jesus that nothing is unclean of itself; except to him considering anything to be unclean, to him it is unclean.

however, the Greek word rendered by unclean carries other meanings. We read the nuances for the word when Peter uses in connection to the vision he had about being offered unclean animals to eat. The word Peter used for "unclean" animal or flesh is not the same word used by Paul in Roman 14:14 to describe what is unclean:

Acts

Acts 10:13-14 EMTV

(13)  And there came a voice to him, "Arise, Peter; kill and eat."

(14)  But Peter said, "Not at all, Lord! For never did I eat anything common or unclean."

The word "common", here in verse 14 of Acts 10, is the same word Paul used in verse 14 of Roman 14. The word "common" is not referenced to "unclean" animal in the Scriptures (or Moses) but the word "unclean" used by Peter is the word referenced to "unclean" animal  that is not to be eaten in Moses.

So, in regards to food and drink, Colossians 2:16-17 does not make the unclean flesh of Moses clean by Jesus Christ nor prevent anyone from drinking wine which is not to say that we can drink as we please because the drunkards will not be saved.

nor thieves, nor covetous ones, nor drunkards, nor revilers, nor rapacious ones shall inherit the kingdom of God. (1 Corinthians 6:10 KJ3)

As you might have understood, depending on your mindset, Paul does not advocate eating unclean meat nor indulging in drinking. Jesus still maintains that not even the dot on the i will not be stricken in the Law. Apostle Paul is in line with Jesus.

Ultimately, in Romans 14:14, besides the negative point even I just made regarding eating unclean meat because of word usage, did Paul really advocate or authorize the eating of food or meat sacrificed to idols in making the point that "nothing is unclean of itself" ? He could not have because of the stance of the book of Revelation against the eating of food sacrificed to idols (Numbers 25:1-3).

Revelation 2:14 (NIV)

Nevertheless, I have a few things against you: You have people there who hold to the teaching of Balaam, who taught Balak to entice the Israelites to sin by eating food sacrificed to idols and by committing sexual immorality. 

Revelation 2:20 (NIV)

[20] Nevertheless, I have this against you: You tolerate that woman Jezebel, who calls herself a prophetess. By her teaching she misleads my servants into sexual immorality and the eating of food sacrificed to idols. 

As it is cautionarily written  in 2 Peter 3:15-16 about understanding Paul, do not jump to twisted conclusion in our zeal to discard the dots on the i's of the Law and the Prophets (Old Testament). 

2 Peter 3:15-16 EMTV

(15)  and consider that the longsuffering of our Lord is salvation--just as also our beloved brother Paul, according to the wisdom given to him, wrote to you,

(16)  as also in all his letters, speaking in them about these things, in which are some things hard to understand, which the unlearned and unstable twist to their own destruction, as they do also the rest of the Scriptures.

Regarding a festival or of a new moon or of sabbaths

Some translations make Colossians read "sabbath days" instead of sabbaths. 

Colossians 2:16 KJV

(16)  Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days:

The King James Version (KJV) translation incites the heated head to reject the seventh day because of the addition of the word "days" to the translation. That is a common practice of the KJV (Matthew 28:1) to insert the word "day" in its translation which leads many astray into false doctrines. 

Yes, the holidays or festivals, the new moon, or the sabbaths (not the seventh day) of Moses are no longer binding because they were shadows of things to come. I will consider the sabbaths (festivals, holidays) in its own section.

Jesus did fulfill the festivals or the sabbaths. So, we are not required to keep any them. Jesus commanded only one observance in Luke 22:19 before He was gone.