亼 represents an inverted mouth, pointing downwards, while 口 is an upright mouth. The characters using it generally bear the idea of gathering and harmony.

  • 合) . . 合he2 means "conjunction, to fit, together". Here 2 mouths are meeting to talk, hence the idea of union. Characters using 合 for its meaning include: 答da2 "to reply, respond" (where 合 can mean "correspond", with the bamboo key used in 符合), 答da1 "to be in agreement", 翕xi4 "to agree", 㒆chi4 "to gather together", 洽qia4 "to blend with, be in harmony", 䆟ke4 'corresponding, appropriate", 恰qia4 "just, proper", 拾shi2 "to pick up, collect, tidy up", 拿na2 "to take, hold" ("close one's hand on something?" since 合 can mean to close by joining two corresponding parts, like windows.) The idea of closing might have generated these variations keeping both the sound and idea: 盒he2 "small box", 蛤ge2 "clam", 颌he2 "jaw".
  • 侖) . . In the character 侖lun2, the mouth 亼 reads a book 册, meaning "discussion, consideration", and nowadays "logical coherence". The variations are: 论lun4, "debate, discourse" (giving 理论 "theory" and 论文 "thesis"), and 伦lun2 "normal human relationships, coherence". They use 侖 both for its sound and meaning.
  • 龠) . . 龠yue4 is an ancient flute, with the mouth 亼, a bamboo flute body which became 冊, and 3 holes 品. The Shuowen comment underlines the multiplicity of sounds and musical harmony: "樂之竹管三孔以和眾聲也 從品侖侖理也". 龠 is also a unit of volume (50ml) worth half of 合ge3 (100ml). 龠 serves as semantic part for the idea of "blow" in 龡 chui4, the archaic form of 吹.
  • 和) . . 和 is today an homonym and nearly a synonym of 合. 和 means "and, union, peace, harmony", with an archaic writing 龢he2 = 龠yue4+禾he2. 禾 is used for the sound. Just like in 龡, 龠 was simplified into 口.
  • 龤) . . 龠 is also used to write 龤 xie2, which is homonym and nearly synonym of 谐xie2 and 协xie2, "harmony and agreement". We can note here the phonetic proximity between 和, 合, 协, 谐, and 龤, close to the middle Chinese pronunciation preserved in Vietnamese as Hiệp (合, 协, 谐, and 龤).
  • 集) . . 亼 can also be read as an archaic variant of 集 ji2, meaning "collection, to gather". In 集 we see birds 隹 gathering on a tree 木.
  • 令) . . In 令 ling4 "order, to command, to cause", the summoned order, the mouth 亼 is giving order to a kneeling man 卩from above. Here "order" bears the dual meaning of "command" and "organization".
  • 命) . . 令 has its variation 命 ming4 "life, fate, command, to assign", same as above, like a cinema director assigning roles.
  • 會) . . 會hui4, traditional form of 会, is composed of 亼, 曰 (yue1: speak), 丷, and 日. Following these components, we can trace back the logical connections of the various meanings: 聚会 to meet up, 会议 to discuss, 理会 to understand, 会 to know how, can, and future certainty. An archaic form of 会 is 㣛ta4 "to walk, to meet, to gather, to be able, to realize". 会 can also be pronounced kuai4 and mean "accounting, to balance an account", again: gathering and harmonizing!

That's it for now!
If you see some mistakes or important missing things so far, let me know. Thanks!

PS: I call (improperly for sure!) "Variations" of a character the combination of a given source character used both for its meaning and sound, together with a specification key. E.g. :
仑 => 论, 伦
合 => 盒, 蛤, 颌
令 => 命
分 => 份
In cases where the sound changes significantly, the resulting character becomes some kind of 会意字 (compound ideogram)， although the construction is clearly in 2 steps (first 亼 + 口 => 合, then 合 => 答, 洽, 䆟, 恰, 拾, 拿, etc.)

References:

  • http://www.chineseetymology.org
  • Pleco Chinese dictionary app