Is there any way to turn off invasions in Dark Souls 2?

Solution 1:

Disconnecting the console from the internet is the only sure way to prevent player invasions in Dark Souls 2.

That said, there are many conditions for both being able to invade and being susceptible to invasions, so your friend shouldn't have to worry too much. In my 72 hours of playing the game, I've been invaded only 3 times, not counting the areas belonging to the PvP-covenants. Those are entirely optional.

Like the comments above mention, you can minimize invasions while online for about an hour by burning a human effigy at a bonfire. The item description for the human effigy mentions this effect:

A warm, soft, shadow-like effigy. Use this item to reverse Hollowing. It also weakens the links to other worlds, preventing invasions and most cooperation. Peer closely at an effigy, and one begins to perceive a human form, but whose form it takes depends on the person looking. #

The Way of Blue supposedly summons available members of the Blue Sentinels covenant to help the Way of Blue player being invaded. I don't believe it matters whether the Way of Blue player is hollow or not, but the Blue Sentinel must be human, wearing the ring and also not fighting a boss or near a boss gate. With all these conditions, I'm not surprised people have seen few protectors these first few weeks after the game is out. Only a portion of players elect to join the Blue Sentinels, and then they both have to sacrifice a ring slot and not lose their humanity to be able to help.

Since your comment mentions the original Dark Souls, I'll add that in that game you would never be invaded if hollow; only in human form. So you could easily play through the whole game without disconnecting your console and never be invaded.

In my experience, invasions have resulted some of the most nerve-wrecking and adrenaline-filled battles in the Souls series. They've also been some of the most memorable, so I recommend not trying to prevent them.

Solution 2:

The simple answer is burn a human effigy in any bonfire. It will temporarily prevent invasions.