The background states that there is no escape even for souls and magic has different effects due to the land being blocked off from the rest of the multiverse.

How do you explain Cleric spells/abilities having power or being refreshed?

Another question: How do you stop the players from committing virtual  suicide by going after Strahd right off the bat?

I found this tidbit:

While in Barovia, characters who receive spells from deities or otherworldly patrons continue to do so. In addition, spells that allow contact with beings from other planes function normally — with one proviso: Strahd can sense when someone in his domain is casting such a spell and can choose to make himself the spell’s recipient, so that he becomes the one who is contacted.

Here: https://www.dndbeyond.com/sources/cos/the-lands-of-barovia#AlterationstoMagic

Strahd would not want to kill them outright, he would want to mess with them and test them a bit first (new blood/souls are rare). He will be watching the players and definitely present them with opportunities to realize how out matched they are before they get to him. See details on his goals and personality here: https://www.dndbeyond.com/sources/cos/into-the-mists#StrahdvonZarovich

You can explain clerical spells being refreshed by saying that the Morninglord and Mother Night, or the Dark Powers of Ravenloft, are granting powers.  Personally, I don't think deities are required for divine magic, you could say that.  Or you could say the gods have enough power to answer prayers, but not to intervene in Barovia, or whatever.

If players really want to go straight after Strahd at level 3, let them bust into Castle Ravenloft.  There they find Strahd, who says what a pleasant surprise it is to see them and invites them to dinner.  They throw down on him and he just phases through the floor.  They literally CAN'T make him fight them until they have the Diary.  He can just let his weakest servants kick them around while he mocks them in magical hologram form.  When he gets bored, he can tell Rahadin to show them the door, and Rahadin can beat them all unconscious.  When they wake up, they're locked outside the castle, naked and with all their gear missing.  Strahd grants them safe passage to the Tser Pool encampment and Madame Eva smacks them on the head for not listening to her.

Quote from TimCurtin >>

 They literally CAN'T make him fight them until they have the Diary.  

 Where is this mentioned? The material is quite extensive.

Tome of Strahd - 

If Strahd sees, or learns from a minion, that the tome has fallen into the party’s possession, all of his other objectives…are put on hold until the book is recovered. When Strahd attacks, his preferred target is whoever has the tome.

Oh I see, not that he CAN'T fight them, just that when the party gets the book, he'll WANT to fight them.

Right.  Nothing a third level party can do will FORCE Strahd to stand still and fight them if you, the DM don't want him to fight them.

So there are times when Strahd will invite the party to dine with him. One of them happens when the party is about lvl 4-5. How do you run that? 

"Hi I'm Strahd, hand over Ireena, kk thanks bye."? There is nothing they can do.

The party is confronted by a horse drawn carriage clad in black, the weather worsens with it's arrival becoming a light downpour as the occasional gust of wind knocks the water about in a strong band of mist. The rain appears to stop just before hitting the carriage and horses as if disappearing into the shadows of the encroaching night.  The horses look more like shadows than they do animal as a formally dressed coachman pulls back on the reigns getting the carriage to stop before you. The door to the carriage is opened up before you as a butler dressed in fine clothing holds aloft the door for you.

"Master Strahd request your audience in the banquet hall for a meal. Please do be so cordial as to accept this invitation, lest the masters attention be placed elsewhere. (Insert name of place/npc they had helped in the past) just now seems to have a moment of reprieve and it would be disheartening if that brief moment of solace was taken away from them."

With that the butler fades into the shadows of the blackened carriage, his message sent and his task complete.

After that you could write it out to explain from Stahds point of view how he and Irene are lovers and she herself has already accepted many romantic dinner invitations from Strahd (a bit of mind control helped this). Strahd was lived centuries and in his backstory he was jealous of his brother for having her. It is possible that he could be taking his time with the "courtship" as it was something he had never had but always longed for. It could be explained from his side that her brother keeps the two apart, simply because of his name and that this is is getting in the way of a romantic relation. He would not want to hurt her brother as that would hurt her and is trying his hardest to do things the "right" way. Deception checks all over the place from him on this if the party wishes to insight.