No, small-leaf spiderwort [Tradescantia fluminensis] isn't poisonous or toxic to animals. The answer isn't so definite in regard to humans. In fact, only one of two things can be said at this point regarding humans. One is that any possible poisonousness or toxicity is low. The other is that what may happen from human contact with the plant's leaves is a fleeting irritation or itchiness of the skin of a susceptible person. That's a general reaction that any spiderwort [Tradescantiaspp] may bring about in humans, not in animals.

Any poisonousness or toxicity of the plant thus far is unknown. Any such indications are at best slight. What looks suspicious in terms of a spiderwort possibly being poisonous or toxic are the plant's oxalate crystals.

No, poison ivy [Toxicodendron radicans] and poison oak [Toxicodendron diversilobum and Toxicodendron pubescens] aren't the same. What they are is related. They share the same genus [Toxicodendron], which is like people who share the same last name. But they aren't in the same species [radicans, pubescens, diversilobum], which is like having different first names.

Something else that they share is a lack of toxicity or poisonousness. Specifically, they both share the presence of urushiol. That oil causes a skin reaction because of irritation, not because of poisons or toxins.