How did Oneness Pentecostalism spread and grow during the 20th century?

I found an article that gives an overview of how the United Pentecostal Church emerged in 1945, although it does not comment on any sort of mission strategy that might or might not have been employed. However, some information may be better than no information, and perhaps others may be able to provide specific information to your very specific questions.

The United Pentecostal Church is a Oneness Pentecostal denomination that was formed in 1945 when the Pentecostal Church Incorporated and the Pentecostal Assemblies of Jesus Christ merged. Their website says that they “grew from 521 churches in 1945” to “4,243 churches and daughter works in 2010.” The United Pentecostal Church claims to be “among the fastest growing church organizations since it was formed in 1945.” Because United Pentecostal Churches are normally congregational in government, there can be some differences among individual churches. As a self-governing church body, each congregation elects its own pastors and leaders. The denomination’s headquarters is in Hazelwood, Missouri.

The roots of the United Pentecostal Church and what is known as “Oneness Pentecostalism” can be traced back to the early days of the Pentecostal Movement, which began in the early 1900s in Topeka, Kansas, based on the teachings of Charles Parham. In 1906 the Pentecostal Movement gained popularity during the Azuza Street Revival led by William Seymour. While it was rejected by mainline Christian denominations, the movement continued to grow and its followers began to form their own Pentecostal organizations or denominations. One of the first was the Assemblies of God, which was formed around 1914.

The teaching that became the basis for Oneness Pentecostalism can be traced back to a Pentecostal camp meeting held in Arroyo Seco, California, either in late 1913 or early 1914. While at the meeting, a Pentecostal pastor named John Scheppe had what he believed was a divine revelation from God. As he meditated that night, he believed God revealed to him that baptism must be done in the “name of Jesus only” and not in the name of “the Father, Son, and Holy Spirit.” Like most cult leaders, his revelation and “new doctrine” did not come as the result of the careful study of Scripture but instead was based on a subjective revelation he believed to be from God. Soon after, several other Assembly of God pastors began teaching this “new revelation” that would become the basis for Oneness Pentecostalism and “Jesus name only baptism.”

As the new “movement” gained followers, it caused a division in the newly formed Assembly of God organization. Recognizing the unbiblical nature of this teaching, the Assemblies of God rejected this unbiblical doctrine and affirmed the biblical doctrine of the Trinity at its Fourth General Council in October 1916. This led to the Assembly of God banning approximately 150 pastors from the denomination, those who had been teaching this unbiblical doctrine. A few months later several Oneness Pentecostal pastors met in Eureka Springs, Arkansas, and started their own organization known as the General Assembly of the Apostolic Assemblies. That was the beginning of the Oneness Pentecostal movement and eventually in 1945 two of the many Oneness Pentecostal organizations merged to form the United Pentecostal Church. https://www.gotquestions.org/United-Pentecostal-Church.html

As for the Assemblies of God denomination, here is a partial quote from another article:

The Assemblies of God is one of the largest Pentecostal denominations, with 57 million adherents worldwide. It was organized in 1914 to promote unity and doctrinal stability among groups that had been influenced by the Pentecostal revivals of the early 1900s, revivals which were the result of a desire to see an increase in God's power in churches and individuals. Many people spent long hours in prayer, seeking a fresh infusion of the Spirit. Following the teachings of Charles Parham, these people were expecting speaking in tongues as an evidence of the Holy Spirit's baptism. The first popularly acknowledged revival was at Azusa Street in Los Angeles, 1906-1909. From that movement, several churches were formed, and in April 1914, meetings were held in Hot Springs, Arkansas, which led to the formation of the Assemblies of God. Eudorus Bell, formerly a Southern Baptist preacher, was appointed as the first chairman of the denomination. https://www.gotquestions.org/Assemblies-of-God.html

I have no information on how the Oneness Pentecostal movement goes about evangelising except to comment on earlier revivals that received a lot of publicity, some of it negative.

Oneness Pentecostals (OP's) accounted for about 1/4 of Assemblies of God ministers before the split between both groups. Most of the OP's ended working with the Pentecostal Assemblies of the World until they separated as well due to segregation. This led most of the white OP's to form many smaller Oneness groups. I believe all groups had some type of foreign mission work overseas but the OP's were hindered by not having as many large organizations as the Trinitarian groups. Mergers were always considered but never fully achieved until 1945 largely due to the great depression and WW2.

Doctrine was a slight problem among some of the OP's since they had all came from a different type of background. Some were stronger on the plan of salvation based on ACTS 2:38 and holiness beliefs while others were not. The most successful merger was that of the United Pentecostal Church, which was founded by two largely white OP's group. The larger growth did not occur until afterwards for most Pentecostal groups including the AOG. But mission groups for both groups were started as early as Azusa Street. OP's group did make a large push for overseas work due to the lack thereof for the first 40 years of their movement.

The Oneness movement spread quickly in it's early in already established works either in the AOG or other denomination that simply came in the Pentecostal faith. So yes there early goal was to convert already established congregations to the "truth". For example, here in some parts of Canada, there are large UPC churches since they were the first Pentecostals here while in another province they are very small. The OP's today grow in church planting efforts and are not growing out of other groups as often as the past.

For the most part the racial line had caused many groups to work separably from each other but there was some percentage of both groups from all backgrounds.