Yes there are implicit laws referenced by the requirement for Gentile Christians to "abstain from what has been sacrificed to idols, and from blood, and from what has been strangled, and from sexual immorality. If you keep yourselves from these, you will do well."

First, we need to know that Jews believed that God placed certain rules in the conscience of all human beings. These are sometimes called the [Noachide commandments](https://www.myjewishlearning.com/article/the-noahide-laws/). It is a fair assessment to say that what we have in Acts 29 is a decision by the elders that Gentile Christians need to accept an updated version of the Noachide Covenant. Among the rules normally included are:

 - Do establish laws. 
 - Do not curse God.
 - Do not practice idolatry. 
 - Do not engage in illicit sexuality.
 - Doo not participate in bloodshed.
 - List item rob.
 - Do not eat flesh from a living animal

Apparently the elders felt that some of these went without saying, as they were already part of Gentile moral norms. But others apparently concerned the elders enough that they felt the need to specify. 

**SEXUAL IMMORALITY**

The OT has many rules regarding sexual immorality. They include laws against adultery and fornication, incest, homosexuality and bestiality. These are fairly well known to most readers.  

**FOOD SACRIFICED TO IDOLS**

The OT Law referred to here is probably Ex. 34:13-15

> You shall tear down their altars... lest you make a
> covenant with the inhabitants of the land, and when they play the
> harlot after their gods and sacrifice to their gods *and one invites
> you, you eat of his sacrifice*

**REFRAIN FROM BLOOD**

This is sometimes interpreted as meaning murder or blood-violence. If so the refence would be found in the 10 Commandments. But this would go without saying. A better reading is that it is a requirement to eat only fully cooked meat. In that case, it is clearly one of the commandments given to Noah. (Gen. 9:3-6)

> Every moving thing that liveth shall be meat for you; even as the
> green herb have I given you all things. But flesh with the life
> thereof, which is the blood thereof, shall ye not eat.

**NOTHING STRANGLED**

This rule has no definite referent in the written Torah, but [kosher butchery](https://www.delightedcooking.com/what-is-kosher-butchering.htm) came to hold that that "the animal must be killed with one clean cut across the throat and allowed to bleed to death." This was apparently already a requirement of the Oral Torah in Jesus' day, meaning the rabbis had reached a basic consensus about it. It would represent the rabbinical interpretation of  Gen. 9 (strangled animals have not yet been drained of their blood) or possibly of Leviticus 11).

These, then, are the specific OT and rabbinical referents to the rules mentioned in Acts 29. They are best understood as a Christian version of the Noachide laws, plus one or two additions based on the emerging consensus of rabbinical thought. I would not say that "This is obviously in response to the circumcision party." The elders were all Jewish Christians and many of them had not yet considered what rules applied to Gentile Christians. It may be more accurate to say these rules were made "in response to the teaching that Paul and Barnabas presented regarding their ministry to the uncircumcised."  Also it  is not completely true that the dietary laws were not required of gentiles. Some of the dietary laws were required: refraining from blood and not eating strangled meat. Not eating food offered to idols falls in an area that might be considered dietary law and/or the law against idolatry.