Is poison venomous and is venom poisonous?
I think you are both confused about terminology, and asking a very broad question. An organism that produces venom is venomous. Poison is not venomous, the black mamba is venomous. Venom is not venomous.

According to the Wikipedia article on venom,


  Venom is a form of toxin secreted by an animal for the purpose of causing harm to another. 


A toxin is a poisonous substance produced by a living organism. The article goes on:


  Venom is injected into victims by means of a bite, sting or other sharp body feature, which differentiates it from poison (that is absorbed, consumed or inhaled).


However, a toxin is a poison, and poisons are defined (by wiki) as 


  substances which cause disturbances to organisms, usually by chemical reaction or other activity on the molecular scale, when a sufficient quantity is absorbed by an organism. (emphasis mine)


So, the definitions are kind of circular. 

From what I understand of your question, you are wondering whether a venom would still be dangerous if it were, for example, ingested rather than injected, as well as whether a poison would still be dangerous if injected rather than ingested (or inhaled, or whatever), and this is where the "Too Broad" category gets applied. There are thousands if not millions of different types of toxins in the world, ranging from full proteins to peptide-based to small organic molecules to completely different structures, such as lipopolysaccharide (LPS, the component of Gram-negative bacteria that causes septic shock). Some may not survive the digestive tract, others might. Some can act through the skin, others can't be absorbed. Inhalation is the next best thing to injection, but probably not for every single one of them, so it's impossible to make broad statements about their efficacy and median lethal dose via different routes of exposure. The exact same thing applies to the "poisons" category - while something that is damaging when absorbed cutaneously, such as methyl mercury, is probably just as damaging directly injected into the bloodstream, it's impossible to say that with certainty about all poisons.