However, if you use the same passphrase, the encryption is as strong as the weakest link. In this case, the weakest link is going to be your passphrase used by your weakest program.
TL;DR: Yes, encrypting triple times can greatly increase your security, although it doesn't have to.
No. Encrypting something three times does not increase the security.
What you should do is to concatenate your 3 different passwords into one password, feed it into a key derivation function and use that key to encrypt your data.
Overall you have the same entropy as when encrypting it 3 times with those passwords individually. But the big disadvantage with your idea is, that the cracking process is being split into 3 parts with less entropy each. This speeds the cracking process up - by a lot.
TL;DR: No, encrypting something more than once does not increase the security at all.