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The short summary for Gallifrey: Time War is that it clears the board of the previous Gallifrey series events and charcters, and explictly sets up the events established in New Who.
Celestial Intervention rids the series of the other Temporal Powers (other species who have mastered time travel), the Daleks having utterly annihilated them all, leaving only themselves and the Time Lords to battle it out.
While also focusing on the increasing influence of the War Council and the first glimpse of the horrific plans, actions and strategies they'll later carry out during the course of the war; Project Revenant - a program to resurrect long-dead Time Lords via their Matrix data, resulting in soldiers and strategists who, can not only regenerate, but be brought back to life to fight and die, again and again and again.
And the horror of the Daleks - reducing a species of 9 billion to 5000 individuals. In just three days.
While mostly set-up, there's some nice character interactions to be had with Romana and Narvin.
Soldier Obscura delves into the more weird time-fuckery that pops up in the War Doctor boxsets. The Obscura, a location which is the result of a previous time war, where reality is so distorted and warped that merely looking upon it will tear mind and body to shreds, forcing everyone to keep their eyes shut.
In an unsual pairing, it's Ace and Braxiatel who are assigned to go to the place - and they make a nice contrast to Ace's previous travels and relationship with the Doctor. Brax reveals to her that in his youth, he had been there before and found a single survivor of this time war - someone who had been blinded and their mind utterly broken.
Ace and Braxiatel both bounce off each other very well, and there's some pretty tense scenes regarding Brax and his very ambiguous character. There's a moment where having murdered his mentor, he is reluctant to perform an action which could destroy a large part of the Dalek fleet, and buy the Time Lords some time, but involves his sacrifice. He admits he is utterly terrified, because that survivor he found, ranting, blinded and mad was not infact from a previous time war...but from the present time war. So the whole area is basically a big fucked-up ball of future timey wimey.
Most surprising of all is Ace - she overhears Brax saying this, and is disgusted by his selfishness - he then forces her to read his mind; all his cowardice and bad deeds - which appalls her even more...so he wipes her mind. Then dumps her on Earth, to possibly tie in with her reference in Death of the Doctor from The Sarah Jane Adventures.
While a perfectly servicable story, it's mostly a character study of Braxiatel - how effective that is depends on the familiarity of Brax and his very complicated backstory.
The Devil You Know continues the temporal weirdness, with a bomb that splits one man's timeline in two. He was in a happy/troubled marriage with his wife/husband. He died. Killed by the Daleks/Time Lords. But he survived. And he has information that the Time Lords want.
Slotting directly inbetween the events of The War Master boxset stories - Beneath the Viscoid and The Good Master - it bridges the two together, and makes good use of the the Master's malevolent nature juxtaposed against Leela's rough, but honest self.
The uneasy chemistry between the Master and Leela is mostly what carries the story. The premise of the man with the split timeline (with both versions existing simultaneously) is fine although not developed in an interesting way, outside of overlapping narration of his conflicting past, but to be fair the story is devoted to the differing approaches Leela and the Master take in trying to convince the man/men in giving them the information they want - the Master through charm and guile, and Leela through compassion and honesty.
And, of course, the Master being the Master betrays Leela and blasts her out into the Time Vortex - presumably for her to appear in a future boxset, or set up her mention in the War Doctor boxset.
Despite being in the Gallifrey boxset, it is very firmly a War Master story, with Jacobi's wonderfully glib portrayal stealing the show.
The final story, Desperate Measures follows Romana and Narvin, as they attempt to both uncover what the War Council is up to, and prevent the Daleks from taking control of Project Revenant.
This is a very continuity heavy story, referencing the early Big Finish Gallifrey-centered audios; Apocalypse Element, Dark Eyes, the other Gallifrey boxsets, and Zagreus, and the TV The Five Doctors, and pretty much every mention of Gallifrey from the RTD era New series, ultimately culminating in the War Council's true goal; the resurrection of Rassilon - First President of the Time Lords, and revered creator of the Time Lord society. The moment is only let down somewhat by my hoping that Big Finish had somehow managed to secretly smuggle Timothy Dalton or Don Warrington in for a brief cameo, but oh, well, always that next boxset 
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Aside from that bombshell, the story is mostly Romana acting with a very contrived stupidity - having secret negotations with the Dalek Emperor saying, basically "The Time Lords will turn a blind eye to you enslaving the universe and expanding your empire, but please don't instigate a time war - the universe will burn and neither of us will win". While the sentiment is fine, the execution feels very clumsy.
In the grander scheme of Big Finish's attempt to cover the Time War, it does feel very much like an attempt to bridge the gap between Classic and the New series - perhaps the most direct attempt as the other Time War related boxsets either skirt round the edges (Eighth Doctor), or are deep into the action (War Doctor/Master), whereas this is explictly the declaration of the war, and the establishment of things to come, brushing aside the old way of things.
I enjoy the Gallifrey series as a whole - nonsense West Wing-style space politics is a goofy enjoyment - some have been better than others, but this feels like a boxset that Big Finish have been wanting to write for a long time (and a long time to come, hopefully), but it depends on personal tolerance for aformentioned space politics.