These are terms used for various philosophical and stylistic approaches or attitudes to writing haiku.
Shasei: Shasei is the principle of "sketching from life" in a haiku, especially advocated by Shiki. The idea is that a haiku should be descriptive of a scene rather than be about abstractions or thoughts on the scene. Furthermore, to be true to a scene, most haiku should be written from actual experiences directly experienced as opposed to imagined scenes. Haiku should also be written while directly observing a scene and not generally from memory (which may distort an element of the scene). Thus, it may be considered inappropriate to write a "summer" haiku during the winter, since you couldn't possibly have been viewing a summer scene at that time.
Karumi: "Lightness", as opposed to heavy-handedness. A light tone suggests talking about very ordinary things and presenting them in ordinary ways. This presents a very personal and comfortable poetry, and is related to the whole haikai approach of producing common poetry, less tied up with court traditions.
Renso: The loose association of disparate images. A common approach to writing haiku is to mention 2 separate images and then in the 3rd line link them together in a surprising or unusual way.
Hosomi: "Slenderness". This principle advocates the use of short, simple, and understated language. Modest and unpretentious.
Fukyo: "Poetic dementia". Basho, and others that followed him, liked to delight in being mad poets. This eccentricity allowed a twisted view of the world in haiku, which was also consistent with the haikai spirit of being less formal and more playful.
Kanjaku: "Supreme quietness". Tranquility and meditation are often sought as a mood for haiku.
Wabi: Austere beauty. Beauty in loneliness and misery, in poverty and simplicity. Wabi and Sabi, I'm told, are not terms used much in the discussion of modern Japanese haiku, but reflect an important mindset and value system in the writing of traditional haiku.
Sabi: Quiet elegance. Elegant loneliness, simplicity, or deprivation. Elegance in antiquity and simplicity.