What's the difference between というものではない、というものでもない and というわけがない?

Apparently they are covered regularly in foreigners' grammar e.g. this or this. I assume you meant というわけではない for the third item.

All three can be translated mostly It is not that ....

Just one example:

• 謝ればいいというものではない : It is not that saying sorry is enough.
• 謝ればいいというものでもない : It is not really that saying sorry is enough.

The former sounds a bit stronger denial/disagreement for 'saying sorry is enough', somewhat suggesting something else must be done. The latter sounds softer, like saying sorry should not be enough, but maybe nothing else should be done either.

というわけではない/というわけでもない are mostly synonymous to というものではない/というものでもない, but like covered here, in a structure with preceding ～だからといって, というわけで{は,も}ない may be more frequent. (～だからといって～というもので{は,も}ない is possible).

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わけない appears as form of ～わけがない, where が is omitted. Means it is impossible that....

For what i know, the first one mean "is not", the second one "Not even" and the third one "There is no reason". They should be used in different context