Flavor of your character, and just doing what you want to do aside - looking in terms of "optimization" or just plain "worthwhileness" - again I'm not saying anyone is 'wrong' who does any multi-classing...
How about this - altogether I'm thinking it could be a multi-class combination "worthwhile" or very close to "as good" as just all levels as a Cleric.
Human. 1st level Barbarian. Then all Cleric after. For example sake - 25 point buy.
Str 14 (or 16), Dex 14, Con 14, Int 10, Wis 16 (14), Cha 14. (If you are willing to figure you can buy or come across a Wis bump before 18th level - you could then at least cast all your divine spells, if not have a bonus spell from Wis mid level on. Then you could go with a little more Str than Wis)
Cleric is likely my favorite class. I really like the Channel Positive Energy. Which again I really like and get the balance aspect of it. But of course makes Cleric even more MADdening (Multi Ability Dependent). Wanting to be more than "just a healer" or waiting to get stout enough spells at later levels to feel more useful in combat (though Magic Weapon, Shield of Faith, and others are good) - I was thinking that 18 rounds of rage from one level of Barbarian (using 1st level and human feat for Extra Rage) would empower some feelings of usefulness to effectiveness to 'heck ya' in combat. Would allow you to use Rage nearly all the time in combat early on and then perhaps all to most of the rounds of a "boss" fight later levels.
And you could go with Community domain or the Restoration subdomain of Healing to remove your own Fatigue 3+ Wis Modifier every day. The thing that first caught my eye and gave spark to this idea.
Looking at other benefits together with the primary combat one of Rage, I'm thinking this may "worth it"
+10 movement. Which would take the Travel domain as cleric. I would say there are some feats, but Swift requires light load... not thinking to go that way.
Martial Weapons proficiency. Could be a big deal depending on what kind of weapons your party comes across or you could be able to acquire.
More class skills. Climb, Swim, Knowledge Nature, Survival, and Perception. Perhaps a few others. I know you could get Perception and others via Traits, but still good. And you would get 2 more skill points at 1st level.
So - as long as you are ok with waiting a level and getting your next set of spells to cast at even levels, not odd. And being one level behind with Channel (which really is a lot of extra healing to start with - or lot of extra damage to undead, especially if you go Sun domain and Sarenrae to go along with the Restoration Healing domain). Then you will have some good benefits to go along with still being a durn good party healer (and undead controller) starting at 2nd level.
I think some unique aspects of the Cleric (or Oracle if they can get Community or Restoration/Healing domain) and the Barbarian make this work well together. Namely that you get a lot of Barbarian benefits from just one level. Whereas say a Fighter - you need to be taking levels to get the more feats. (I know there a lot of great other things Barbarian levels get you, that this would miss out on.) All the above plus that you can take Extra Rage as feats at later levels without taking any more levels in Barbarian. I would think you would like to take Selective Channel, Quickened Channel (maybe put a skill point in Knowledge Religion at 1st as a Barbarian so you can do Quickened Channed with 5 ranks in it at 5th level), and possibly Extra Channel before you start going more Extra Rage. 18 rounds at 1st should last you up to 5th, 7th, or 9th I would think. And on the Cleric / Oracle side - the fact that even with one less level, you are still likely a great healer for the party. And still ok with the control or other spell aspects you have. The sort of great at healing, ok at a lot of other things (other than a variety of skills) aspect of them I think uniquely suits Cleric / Oracle to lose a level to multi-class without dropping it's 'power' level down as much as it would some other classes. Again - if you are getting a lot of gain from that other level, as I think you are here.
The other way to do this that I don't think is nearly as appealling, and again cleric is my thing, but I can see how getting rid of your own Fatigue at 1st or 2nd level rather than 16th or so for Tireless Rage could be good - would be one level of Cleric for Community or Restoration / Healing domain and then Barbarian after.
My orginal thought was for a Dwarf version. The +10 movement together with Dwarves movement not being affected by armor or encumbrance is very good. But 12 vs 18 rounds of rage with no plans for more than one level of Barbarian. Really it was the 6 more rounds and perhaps most of all the Dwarven issue with Cha that eventually pulled me to Human. Though a Dwarf or other race could also do well. And just realized you could take more Extra Rage feats down the line (just have to have the class feature to take it, not gain a level in the class) - so very viable.
Thoughts? Agree or disagree that this might be a multi-class combination that is "worth it" or "pretty close to as good" even for the most min/max, character optimization minded out there? Something you might want to try? Any cleric lovers thinking they might want to use it to give some combat umph to their next cleric?
Thanks in advance to constructive, thoughtful comments. I won't take offense to "not worth it - all cleric levels is more helpful to the party or just more effective character overall" especially with some fleshing out - I am after all asking for such consideration. Also "do what you want with your character" - I fully agree with, but not really the input I'm seeking here. And a similar final note to "This is the kind of 'roll-play' discussion I hate" - I can understand, and apologize in advance for bringing down your mood. Hope you enjoy other discussion elsewhere more.