Here is an amazing strategy to find Abra that served me well, allowing me to recruit the three Abra I needed. Go to Solar Cave, bringing with you, along with your usual assortment of items, eight Radar Orbs, two Escape Orbs (in case one becomes sticky), a Friend Bow, and a Stamina Band or Tight Belt. On each of the first eight floors, use a Radar Orb and then sit still with your Stamina Band or Tight Belt equipped while holding "A" and "B." You will see a plethora of wild Pokémon appearing on the floor. Knock out any that enter your room, but keep an eye out for any red dots that sit in one spot instead of moving. While one of these dots will occasionally be a random sleeping Pokémon, many of them will be Abra. Why is this? When an Abra enters the floor, it will always be asleep; as a result, only the stationary red dots have a chance of being an Abra. Keep waiting in this way until you either get an Abra (at which point you should warp out with an Escape Orb) or see a windstorm approaching; if the latter happens, enter the next floor, use another Radar Orb, and repeat the process. The search will seem much quicker, as you will know exactly what wild Pokémon have a chance to be an Abra.
By the way, if you don't want to search any longer than necessary, you could recruit only one Abra and obtain the other two forms by recruiting the rather common Kadabra deep within Solar Cave. However, keep in mind that your leader must be at least Lv. 90 (or Lv. 50 with a Friend Bow) to have a chance of recruiting it.