If the Cleric casts Mass Healing Word, targeting each of the 4 party members, how many times would the Cleric gain HP equal to 2 + Spell Level?

I would argue only once, because the trigger for Blessed Healer is "When you cast a spell...". You only cast one spell, so you'd only get healed once.

Taken further, would the Blessed Healer effect be prevented if the Cleric targeted himself with Mass Healing Word, in addition to the other 4 members of his party?

That's easier to answer. I'd say no, the effect is not prevented, since casting mass healing word to heal at least one person other than yourself clearly satisfies the requirement for Blessed Healer.

Targeting the same creature multiple times simultaneously with the same effect causes the creature to be affected still only once

That is, this GM would rule that just because an effect can be used one time against multiple targets doesn't mean that the same effect can instead apply multiple times against one target and yield multiple results.

While it can be technically lawyered that a spell that affects multiple creatures can, instead, affect the same creature multiple times, that notion doesn't yield positive results in actual play (i.e. you'll earn a book to the noggin not applause). And, as you can see from broaching the question here, even bringing up the idea is anathema to some.

To put this negative reaction in perspective, let me employ an analogy: a game show contestant is allowed to pick two cars. While most contestants will pick two different cars, this contestant baffles host and studio audience by picking the same car twice, technically picking two cars: this car and this car again. Although this impresses the game show's lawyers, and the sponsor's pleased at the prospect of only having to provide one vehicle, this makes for lousy ratings. Seriously, don't do this: you don't want to make Drew Carey—or the GM—angry.

That said, the spell mass cure light wounds targets "one creature/level, no two of which can be more than 30 ft. apart." However, once the caster has picked that one creature to be affected, picking that same creature likely runs afoul of of Combining Magical Effects: the creature is supposed to realize simultaneously enough the same spell's effect multiple times, something the game usually either rejects outright or accommodates grudgingly (by mandating only the most recent, most beneficial, or most detrimental effect occurs).

With that in mind, a GM could allow a lone creature to be targeted multiple times by a mass cure light wounds spell then have only the highest individual result affect the target… or even have the target affected uniquely only once, the GM mandating all creatures that the spell would've affected would've been affected equally.

Compare the spell mass cure light wounds with the spell wail of the banshee: the wail targets "one living creature/level within a 40-ft.-radius spread," and "[c]reatures closest to the point of origin are affected first." This does not mean if a Wiz20 catches but two creatures in that 40-ft.-radius spread, the wizard can force those two creatures to make 10 successful Fortitude saving throws each or die! Each affected creature instead makes 1 saving throw, and the remainder of the spell's effect is wasted. (By the way, here's a Paizo messageboard discussion about the spell wail of the banshee.)

This GM urges that unless a spell or effect says otherwise, a decision to use the spell or effect against less than than its maximum number of targets doesn't make the spell or effect's power greater against the targets the spell or effect is used against!

(I could find but this lone 2011 Paizo messageboard thread discussing the idea of picking the same target multiple times for an effect that affects multiple creatures. The topic doesn't seem to warrant serious consideration.)