The Eights describe the movement of energy, and in that way they have qualities of both air (movement) and fire (energy/creativity) in all the suits. The Tree of Life association is with the Sefirot Hod, "Splendor" or "Glory". This echoes the qualities of air and fire, of magic and power connected to a world close to, but above, our own world.
Mercury in Sagittarius
The Eight of Wands is reveals an abundance of this energy--swift, powerful, but also potentially quickly depleted. The lightning bolts in the Thoth deck and the flying, arrow-like staves in the Waite-Smith both allude to this quality of powerful energy being released or applied in a quick burst.
Saturn in Pisces
In the Eight of Cups, the intuitive and dreamlike waters of Pisces and stern hand of Saturn slow and mute the air and fire. This card has the quality of "feeling something out" with one's intuition and emotions. More specifically, it often comes with the "feeling out" of one's dreams or fantasies of emotional fulfillment; for example, what it would feel like to have the ideal relationship, the most fulfilling work, the most beautiful and secure home, and so on. The danger in this is potentially becoming lost in reverie and not acting upon a particular path to actually manifest the vision. It may also indicate self-sabotage in completing or accepting one's fulfillment.
Jupiter in Gemini
The Eight of Swords signals a blockage in the movement of energy, or the energy scattering in many different directions and dissipating. This blockage could come from many sources, but there is usually a mental, analytic, or frame of reference component to the blockage; that is, someone's thoughts or way of looking at the situation can be contributing to the blockage. This could be in the vein of indecision, a difference of opinions, legal action, etc. The energy of the benefic Jupiter bringing fire and fortune is scattered in the indecisive Gemini. Much like the cups, the movement of energy doesn't find an outlet to fully express, but this time through thought rather than feeling.
Sun in Virgo
The Eight of Disks slows down the movement of air and consolidates the fires of creativity. Generally this is a positive, supportive action recommending patience and nurturing growth. The movement of energy is grounded and takes root and can manifest in something stable and long-lasting.