Austro-Asiatic
In particular, Cambodian and Vietnamese are both Austro-Asiatic. Traditionally, as noted in the comments, Cambodian is classed with the Mon language of Burma, under Mon-Khmer (as is faintly evident on the map Mon languages seem to have been spoken in what is today central Thailand before their replacement by Thai). There are also Austro-Asiatic languages on the fringes of southern China, though again the map is very illuminating, as the pattern of fragmentation is often indicative of marginalization and language replacement. Finally, there are Austro-Asiatic languages spoken in India, and among the indigenous people of central Malaysia, who are often termed Negritos (as well as the Nicobarese).
Tai-Kadai
As you can see the Thai are thought to have come from modern Mainland China, somewhere south of the Changjiang (Jiangzi), and migrated under pressure from Han expansion during the Tang Dynasty into Southeast Asia, basically invading areas controlled by the Mon-Khmer speakers and also the Sino-Tibetan speaking people of Myanmar. They absorbed quite a few of these groups. The Thai especially absorbed a lot of Khmer as well as massive amounts of Chinese migrants.
Austronesian
They likely originated in present day Mainland China and moved to Taiwan, where they branched out across the Indian and Pacific Oceans…from Africa to Easter Island (Polynesia). As they branched out they ran into “Negrito” like people. Negrito people look very similar to African Pygmies, and thought to be indigenous to various areas of Southeast Asia and areas of South Asia, possibly the representative of the phenotype of the first modern people in the region (possibly). Filipino and some Indonesians seemed to have absorbed a lot of Negritos. Eastern Indonesians also have admixture with Papuan-like people, that are now centered in New Guinea, but also have been known to have likely migrated in the local area (Northern Australia, and likely Eastern Indonesia) in the past.
GENETICS
There have been a few studies on this, here are some of the highlights…
Contrasting Linguistic and Genetic Origins of the Asian Source Populations of Malagasy
Genetic distance (MY FAVORITE, it really shows the distance between all the groups and admixture:
Language, genes, & peoples of Southeast Asia - Gene Expression
Some conclusions:
It is pretty clear that Malay and some Indonesians have some components are Mon-Khmer, but Filipinos (also Austronesian speakers but a bit more distant in geography do not).
Although not represented above, Cambodians (Mon-Khmer speakers) also have some admixture from South Asia (likely India), due to ancient contact. It is a low % but well spread out over the population, so likely quite ancient. It is mostly from the male side.
Tai and Vietnamese (so both Austronesian and Tai-Kadai) speakers have quite a bit of Northeast Asian admixture. In the case of Tai this could have been present since ancient times., but in the case of Vietnamese and Tai it was greatly increased due to migration of Han Chinese in historic times to Thailand and Vietnam respectively.
Zhuang are Tai speakers but they appear very much like Southern Chinese genetically…partly because most Southern Chinese have some Tai component, as Tai people were Sininized in historic times during the Han expansion, but there has also been gene flow between the groups (in both directions).
There are Mon-Khmer speakers in India that clear Altaic, which was probably due to ancient admixture coming from Northeast Asia before this group migrated into Eastern India and brought rice farming culture.
In any case it is pretty clear that language group does highly correlate with genetic affinity most of the time, but not always. There are groups like the Zhuang (Tai speakers) as compared to Thai, Javanese as compared to Filipinos.
There are groups not mentioned in the question, like Melanesians (Negritos in Eastern Asia and Pacific) and Hmong that are quite unique and form their own groupings, this could be due to small population size (genetic drift) or something else…
Other findings
1 We see that the Cambodians are a hybrid of a population like the Dai of South China, and something somewhat Indian-like, but not totally.
2) The Vietnamese have a very faint gene flow from the Cambodians. Some of the samples which were Vietnamese look to me like they were ethnic minorities. I left them in because that is part of Vietnam’s genetics. They may simply be assimilated minorities or Khmer.
4) The Negrito ancestry among Filipinos is pretty obvious in the gene flow.
Language, genes, & peoples of Southeast Asia - Gene Expression