If we expand the contractions, we get:
* It's not something I had ever heard of before I came to Beijing.
* I have never heard of that before.
Sentence 2 has an implied "now" after before.
* I have never heard of that before [now].
Not the different tenses after we expand the contractions. Had vs have.
Sentence 1 is "Past Perfect Tense", which means "an action that took place in the past before another past action". The past action was coming to beijing. So we use 'had' because the action of not hearing took place before the past action of coming to beijing.
Sentence 2 is "Present Perfect Tense", which means "an action that happened at an indefinite time in the past or that began in the past and continues in the present". Since 'now' is implied, the past action of not hearing began in the past and continued up to right now. We would use past perfect tense instead for 1 minute ago. 'I /had/ never heard of that before 1 minute ago.' "I /have/ never heard of that [before [now]]." Here, both 'before' and 'before now' are optional.
Also "that" essentially refers to the same thing as "it's not something". So the sentences could also be written like this, with the key blocks highlighted:
> [It's not something] I had ever heard of before I came to Beijing.
> I've never heard of [that] before.
> [That is not something] I've ever heard of before.
> [It's not something] I've ever heard of before.
All are common enough to use. I would generally use the second example, but would change the past/present perfect tense depending on if I were referring to now, or before coming to beijing.
reference:
http://leo.stcloudstate.edu/grammar/tenses.html