utensil, vessel, receptacle, implement, instrument, ability, container, tool, set
器 centers on a physical object that holds or does something: a container, utensil, or tool. The ability sense extends this idea to a person's capacity to hold or perform a role.
器 combines 哭 (a dog-like shape with mouths) and 吅 (two mouths), historically suggesting a vessel or container with multiple openings. The exact development is uncertain, but the vessel meaning is well established.
The top 哭 looks like a dog with four mouths, and the bottom 吅 adds two more mouths. Picture a complex vessel with many openings, like a multi-spouted container or a tool with several ports.
For キ, imagine a key-shaped tool fitting into a special container: key -> キ, and the key unlocks the vessel's many openings.
bowl; vessel; container
weapon; arms; ordnance
arms; weapon; ordnance
device; equipment; machinery; apparatus
musical instrument
container; receptacle; vessel; packaging
utensil; implement; tool; instrument; appliance; apparatus
nuclear weapon
internal organs; viscera
tableware
skillful; skilful; adroit; dexterous; dextrous; deft; nimble; handy
clumsy; awkward; unskillful
organ
dangerous weapon; lethal weapon; deadly weapon; murder weapon
pottery; earthenware; ceramics; (soft-paste) porcelain; china
stone implement (e.g. stone age arrowheads); stone tool
earthenware
small arms
urinary organs
meter; gauge
ceramics; pottery and porcelain
firearms; guns
hearing aid
blunt weapon
receptacle; container; vessel
string instrument; stringed instrument
porcelain; china; chinaware
percussion instrument
tools and materials; equipment and materials
electric (goods)
lacquer ware; lacquerware; lacquer work; lacquerwork
(telephone) receiver
instrumental music
water heater; water boiler
chemical weapon
respiratory organs
circulatory organ
wash basin; wash bowl (incl. portable bowl in a public bath)
digestive organ
fire extinguisher
rice cooker
alarm (fire, burglar, railroad-crossing, etc.); sensor
circuit breaker