Ill write more about other factions such as the Karen later.
Eastern Groups
Karen groups:
Karens are, like other ethnicities, a grouping of different tribes. They traditionally lived in an area called the Karen Hills. They are typically separated into two major groups based on dialect: the Karen (occasionally called White Karen) and the Karenni (Red Karens). Karen history has been significantly affected by British imperialism and missionary activities, and this is reflected in their current geopolitical position.
Karen National Libration Army:
The KNLA is perhaps the most famous of the EAOs, It's (and that of the Karen ethnicity's) dominance and its fall is perhaps a textbook example of the hubris of Christian imperialism and colonialism.
Karens were the most predominant hill tribes recruited by the British as a "martial caste." They were intensely Christianized and played a significant role in Burma's colonial civil administration due to the missionary efforts that helped standardize their language. The term 'Karen' is effectively an invented term used by these urbanized, Christian Karens as a unifying label for their ethnicity.
At Burmese independence, they composed 27% of the army, including most of the officer corps, and formed the governing elite, despite representing only about 10% of the population. In contrast, the Bamars made up 75% of the population but accounted for just under 50% of the armed forces, especially when considering the new army incorporated the previous Japanese Burmese Independence Army (prewar Bamar percentage in 1937 was much lower at 12%).
The British left the armed forces in a somewhat feudal state with separate Bamar regiments, Karen regiments, Chin regiments, Kachin regiments, etc. The Chief of Staff, Smith Dun, was a Christian Karen, and both the Chief of the Army and the Chief of the Air Force were also Karen.
This fragmented system was, of course, unacceptable to the new government due to doubts about its loyalties and its ineffectiveness in fighting the CPB. As a result, they began working on centralizing the military. Ne Win (the future Prime Minister and President through a coup) replaced Dun in 1949. Through further reforms and replacements, the modern centralized armed forces would emerge around 1955.
In the meanwhile, ethnic conflicts were flaring up, and dismissed and removed Karen soldiers gradually coalesced into the Karen National Liberation Army (KNLA). Inheriting intact military organizational capabilities, they were able to take over towns like Mandalay and laid siege to Rangoon. It was thought that the new separate Karen state (Kawthlooi) would actually include Rangoon. (Rangoon was actually a city with a predominantly Indian population at the time, where "Indian" included Bangladeshis, Pakistanis, etc.)
However, the Bamar population began to arm themselves (which would form the basis for many right-wing militias today), and the KNLA was gradually overwhelmed by the majority population in the plains and retreated to their southwestern hills. By the 1970s, the KNLA was quite clearly in decline, forced into the hills by the strengthened and centralized armed forces.
By the 1990s, the once powerful KNLA had started to erode, dealing with various strongman cults, a splinter faction led by two 13-year-olds, and, of course, the culmination of their current downfall, the Democratic Karen Buddhist Army. The urban Christian officer core of the KNLA, once forced into the mountains, had been recruiting heavily from the local Buddhist population, who complained of discrimination and mistreatment. Things came to a boiling point when over a thousand defected in to the DKBA, which allied with government forces and captured Manerplaw, an important crossing point on the Thai border. This significantly affected their revenue and logistics since they had been taxing the crossing and relied on it for arms and munitions. The KNLA is now a very splintered faction, with different brigades operating separately from one another.
These days, while having experienced fighters, the KNLA is deprived of significant weaponry. The end of the Cold War and significant Western support means they are often fighting with Vietnam-era M16s and ancient pineapple grenades. They are also very splintered, with its brigades not operating as a coordinated force and descending somewhat into warlordism.
Through their missionary contacts, they have excellent Western PR, with many missionary groups agitating about the suffering of these poor tribal Christians. They also use it to recruit former Western special forces to serve as "medics," but with little success. They were recently incorporated into the PDF, but this is irrelevant as the KNLA can't coordinate among themselves, much less with other groups.
Karenni Groups:
The Karenni group lives in a more isolated part of the country than their Karen cousins. Their chieftains were able to secure recognition from the British and were governed separately for some time. Eventually, they were incorporated. They share a somewhat similar history to their Karen cousins, but since they are a bit more inland and have a different dialect, they were Christianized later. Their smaller numbers (about a third of a million Karenni compared to some 4 million Karens) meant they were never as politically dominant as the Karens
Their armies go by different names, such as the Karenni Army, Karenni Nationalities Defense Force, Karenni Revolutionary Union, etc. In any case, they are undertrained and under-equipped, like most PDF forces. The Karenni are about 50% Christianized and thus receive Western PR. Their actual effectiveness is questionable, but when you start from the bottom, the only way you can go is up.
Mon National Libration Army:
The Mons are an ethnic group that speaks an Austroasiatic language, making them an outlier among all the Tibeto-Burman-speaking groups. They likewise seek separatism and autonomy for themselves. However, when the KNLA retreated to the southeast and began to collect tolls in the area, the Mons signed a ceasefire agreement with the government and cooperated in fighting the KNLA. They did not accept incorporation into a BGF and thus remain independent from the government. They currently maintain their conflict with the KNLA, albeit at a much lower intensity. They mostly focus on localized security and try to remain neutral in the current conflict between the opposition and government, negotiating with both sides.
I left out a lot of other groups like Ta'ang National Liberation Army, Shan State Army North, Shan State Army South, etc. To go through them all would be too difficult, and they tend to have similar stories. I avoided topics like drug trafficking, child soldiers, and displaced persons and refugees because they tend to divert the focus of the conversation to the point where it simply becomes 'drugs are bad, child soldiers are bad,' etc. I hope this is useful, and I accept any corrections.