Wolverine gets some new abilities

[FennerMachine]

Wolverine is granted some new abilities in addition to his existing ones. He keeps his personality accepting that these new abilities could alter his personality over time.

She-Hulk style transformation and strength (the stronger he is, the stronger the transformation).
Shape shifting abilities – including his Adamantium (pointless if he couldn't).
Professor-X level telepathy.

Who is the strongest character Wolverine could defeat or hold his own against?
How powerful do the X-Men team now become?

[big_adventure]

Well, he personally stomps basically anyone who he can hurt and who can't just speed-blitz his ass.

He'd dominate most of the Avengers, for example, he could solo the FF, he could solo most X-teams (basically, any that don't include Hope, Nate, a tough version of Jean or Rachel). He couldn't really solo most good Avengers teams, because good Avengers teams include Thor or Captain Marvel/Photon/Spectrum, and they blitz-stomp him.

Sabertooth's next birthday crap would most definitely be his last.

All of his personal rogues are mincemeat, or drooling idiots locked away for life somewhere (or, ThugReed style, convinced that they are cows).

Many X-Rogues are going down as well, though he's still going to have his hands full against a fair number of them - Bad Magneto still has the helmet and Logan's adamantium, Sinister/Exodus/Poccy are not people he can mind-whammy and they are awfully potent in other ways.

Given that, at various times, he's gone into vendetta mode against Hydra, AIM and the Hand, we can figure that none of those organizations exist anymore. Logan's not shy about killing, and we just made him into a MUCH better killer.

[The Drunkard Kid]

Emma gets completely wasted for a month at the idea of Logan being a stronger telepath than her, but afterwards the two of them spend a lot of quality time figuring out nasty things to do to his Rogues Gallery.

[T-1000]

Adding Xavier telepathy alone is just overkill. Frankly, Xavier has always been among if not the most powerful X-man of all time, he just doesn't use his powers because of the temptation that they present.

[Surtur]

Sigh, when I saw the title I was hoping "being interesting" would be one of his new powers.

[Dr Will Hatch]

Wolverine is granted some new abilities in addition to his existing ones. He keeps his personality accepting that these new abilities could alter his personality over time.

She-Hulk style transformation and strength (the stronger he is, the stronger the transformation).
Shape shifting abilities – including his Adamantium (pointless if he couldn't).
Professor-X level telepathy.

Who is the strongest character Wolverine could defeat or hold his own against?
How powerful do the X-Men team now become?

If this had said "Wolverine can now turn into She-Hulk", I might start reading his comics again. Holy moley, that would be an interesting power.

Per your scenario, he loses what's left of what DOES make Logan interesting and turns him into just another run of the mill overpowered jackass.