Welcome to Just Answer. The bird of paradise plant seeds are considered toxic to dogs and cats. The toxic signs are - oral irritation, intense burning and irritation of mouth, tongue and lips, excessive drooling, vomiting, diarrhea, difficulty swallowing and incoordination is possible. So as far as toxicity goes, it isn't severe as far as fatality situation. If he was to eat a ton of them he could have some significant intestinal upset.
I would say as long as you pick up as many as you can, and he doesn't eat that many - he should be ok.
Ok. Sago and other Cycad or Zamia palms are problematic as far as toxicities. The Sago being very bad! But this is the very small (ornamental - it is now in many houses as a house plant that owners don't realize is bad).
The large palms that your describing shouldn't be toxic. Just make sure the seeds themselves don't get swallowed and cause a foreign body. That is where most of the time problems arise. They get ingested and stuck somewhere.
The oleander toxicity is potentially a much more serious one as it can cause heart issues - all parts of the plant have a highly toxic cardiac glycoside much like digitoxin, and can cause diarrhea (possibly bloody), sweating, incoordination, shallow/difficult breathing, muscle tremors, recumbency, and possibly death from cardiac failure.
In your situation, I would try to make sure that a majority of the leaves are out of the yard when you let him out. If he's out there and eats one, the best thing you can do at home is to make him vomit right away to reduce toxicity.
To get your little one to vomit:Three percent hydrogen peroxide is quite effective in making dogs vomit. Be sure to use three percent peroxide. Despite the label indicating that hydrogen peroxide is toxic, it is safe to give to dogs for this purpose. It is considered toxic since it induces vomiting and therefore does not stay in the body.The appropriate dose of hydrogen peroxide is one teaspoon per 10 pounds of body weight. One teaspoon equals 5 cc or 5 ml. Once the hydrogen peroxide is given, walk your dog around or gently shake the stomach area to mix the peroxide with the stomach contents. Vomiting should occur within 15 to 20 minutes. If no vomiting occurs, you can safely repeat the three percent hydrogen peroxide once.
This toxicity is one that if just one that we don't have a specific amount needed to cause the worst of signs. Obviously the more eaten the worse the potential. If a lot are consumed, I would recommend having him then taken to the ER clinic for charcoal administration and hospitalization for observation of heart problems.