The Order of Special Full-Time Servants appears to be a religious order of Jehovah's Witnesses. What is a religious order in the context of Witness theology? Is it theologically meaningful at all? To what purpose do people join this order? When do they leave? (Do they leave?) How does the whole thing work?
The different types of full time servants among Jehovah's Witnesses are:
Regular pioneers usually spend 70 hours a month in the field ministry. Some serve in a congregation where the need is greater.
Special pioneers usually spend 130 hours a month in the field ministry. They are often assigned to a congregation where the need is greater.
Circuit overseers visit congregations to help them improve in their ministry and encourage them in other ways.
Bethel family members serve in a branch office or a translation office. They help provide literature and direction for the ministry in the territory that is supervised by the branch.
Missionaries are usually assigned to serve in another country. Many missionaries spend 130 hours a month in the field ministry
International servants and volunteers go to various countries to assist with the construction of branch offices, remote translation offices, Assembly Halls, and Kingdom Halls.
Kingdom Hall construction servants are trained to build Kingdom Halls and assist with other construction projects in their own country.
For additional information see the following article from the September 2014 Watchtower: https://www.jw.org/en/publications/magazines/ws201409/remember-those-in-full-time-service/#link0
As for the specific title of your question there is indeed a group called the Worldwide Order of Special Full Time Servants. According to the April 2017 Watchtower:
Currently, there are some 67,000 members of the Worldwide Order of Special Full-Time Servants of Jehovah’s Witnesses. Some perform Bethel service, others engage in construction or in circuit work, serve as field instructors or special pioneers or missionaries or as Assembly Hall or Bible school facility servants. They are all bound by a “Vow of Obedience and Poverty,” with which they agree to do whatever is assigned to them in the advancement of Kingdom interests, to live a simple lifestyle, and to abstain from secular employment without permission. It is not the people but their assignments that are viewed as special. They realize the seriousness of humbly living up to their solemn vow for as long as they remain in special full-time service.
I spent a great deal of time searching for an answer to this that doesn't make it sound like a scam to avoid taxes and enjoy the benefits of being treated as a religious institution, but I couldn't. As is usually the case, it's a lot easier to find information from those that stand against the Jehovah's Witnesses than it is to find positive information about them.
According to outsiders it's little more than a tax dodge as stated in these first few links.
However... The most complimentary description was found in a legal document from the Oregon Judicial Department Apellate Court This seems a little less inflammatory. It describes them as people that have simply dedicated themselves to ministry, and therefore would function in a way that assists the Church. As such, their right to tax-exempt status is less clear.
However, this question isn't (as far as I know) about their tax-free status, but about what they are, and what their function is. Unfortunately, the following is the best, least inflammatory description I could find. Since they don't have information about themselves online anywhere, this is what I'm settling for providing. It's not first-hand from them, but presumably it's based on first-hand interviews with lawyers that are familiar with the defendants. It's better than nothing.
Before explaining the particular facts of this case, it is helpful to give some background information on the organizational structure of Jehovah's Witnesses. Jehovah's Witnesses worship within congregations, each of which meets within a Kingdom Hall. (2) Each congregation of Jehovah's Witnesses is located within a circuit. Taxpayer, for instance, is one of approximately 22 congregations located within Oregon Circuit 6, which stretches from Beaverton to the coast and from Tillamook to Astoria. (3) Congregations are led by Elders and Ministerial Servants, both of whom are volunteers and generally have secular employment. Elders minister to other congregation members and train Ministerial Servants to assume increasing responsibility within the congregation and larger organization of Jehovah's Witnesses.
Higher up in the organizational structure, Jehovah's Witnesses are led by members of the Worldwide Order of Special Full-Time Servants of Jehovah's Witnesses (the Order). Members of the Order take vows of obedience and poverty, eschew secular employment, and dedicate their lives to overseeing and directing the spiritual needs of Jehovah's Witnesses. In return, the Order promises its members housing and a minimal stipend to cover living expenses. There are several types of Order members, including Circuit Overseers and Special Pioneers. Circuit Overseers live within the circuit to which they are assigned and work with congregation leaders to meet the needs of each congregation. Specifically, Circuit Overseers supervise the work of Elders and Ministerial Servants by annually traveling to and spending at least a week with each congregation within the circuit. Circuit Overseers usually stay in the homes of local Jehovah's Witnesses as they travel from congregation to congregation. Substitute Circuit Overseers, who fill in for Circuit Overseers when they are temporarily unable to fulfill their duties, are rarely Order members, but instead are usually secularly employed Jehovah's Witnesses. Regarding Special Pioneers, the only kind relevant to this case are those who are on infirm status. Special Pioneers on infirm status, few in number, are often ex-missionaries. They generally do not travel but rather stay with one congregation and serve that congregation, as well as the circuit and religion as a whole. However, few congregations have a Special Pioneer, whether on infirm status or not, assigned to them.
Full time ministers of Jehovah's Witnesses are those that spend a minimum of 70 hours per month in some form of Christian service. By far the vast majority of these ministers also work and pay taxes.
A proportionally small number work in the Jehovah's Witness Branch offices and are offered logding and a small allowance and others are missionaries and travelling ministers that also get a small allowance from the organization.
Whether these individual pay taxes dépends on the law of each country but many do not because their income is so very low they are non-taxable.
Members of the Order take vows of obedience and poverty, eschew secular employment, and dedicate their lives to overseeing and directing the spiritual needs of Jehovah’s Witnesses.
The above statement, taken from an Origon tax court decision, is incorrect.
No one is asked to take any vow of poverty nor to “eschew” secular employment, nor do they “dedicate their lives to overseeing and directing the spiritual needs of Jehovah’s Witnesses.”
Source: The Watchtower, October 1st, 1973, p. 607, “Questions From Readers.”
It should also be noted that vows were something spontaneous, and hence unrequested, unsolicited. They were not something set forth as a general requirement for all who would enjoy a certain privilege or enter into a certain relationship. Hence, one’s becoming a disciple of Christ Jesus and fulfilling the requirements that are set for all persons, including repenting and turning around and making public declaration of one’s faith, and being baptized, do not involve a “vow” in the Scriptural sense.
Nor are Scriptural vows to be compared with the so-called ‘monastic vows’ that persons in later centuries were required to make in order to gain admittance into certain religious orders of church organizations. Those vows of ‘chastity, poverty and obedience’ placed those vowing under obligation to the religious orders and served those orders as a means of exercising control over their adherents. Higher church officials could absolve persons from certain types of vows, but with some vows release could be gained only through the titular head of the church, as in the papal arrangement. These, then, are not Scriptural vows, for Scriptural vows were entirely spontaneous and personal, between the individual and God. Furthermore, under the Law, although a woman’s vow might be disallowed by her husband, or father (within a certain time after being made), in other cases no human could grant one release from a Scriptural vow.—Num. 30:3-15.
From this it is apparent that many so-called “vows” of today are not really such in the Scriptural sense.
Their dedication is to Jehovah God.