Incompatible pointer types assigning to 'id<AVAudioPlayerDelegate>' from 'Class'

You've declared your method as a class method, and you're trying to use the Class object as the delegate. But you can't add protocols to Class objects.

You need to change playAudioFromFileName:... to an instance method and create an instance of Utility to use as the delegate. Maybe you want to have a single instance of Utility shared by all callers. This is the Singleton pattern, and it's pretty common in Cocoa. You do something like this:

Utility.h

@interface Utility : NSObject <AVAudioPlayerDelegate>
+ (Utility *)sharedUtility;
@end

Utility.m

@implementation Utility

+ (Utility *)sharedUtility
{
    static Utility *theUtility;
    @synchronized(self) {
        if (!theUtility)
            theUtility = [[self alloc] init];
    }
    return theUtility;
}

- (void)playAudioFromFileName:(NSString *)name ofType:(NSString *)type withPlayerFinishCallback:(SEL)callback onObject:(id)callbackObject
{
    ... 
    audioPlayer = [[AVAudioPlayer alloc] initWithContentsOfURL: [self getResourceURLForName:name ofType:type] error: nil];
    audioPlayer.delegate = self;
    ...
}

@end

Usage

[[Utility sharedUtility] playAudioFromFileName:@"quack" ofType:"mp3" withPlayerFinishCallback:@selector(doneQuacking:) onObject:duck];

When you don't need an instance of a Class, just manually get ride of the warning:

audioPlayer.delegate = (id<AVAudioPlayerDelegate>)self;

On the other hand, please note that if you need a Delegate, it means you should have an instance of a Class as a good coding practice instead of a static Class. It can be made a singleton easily:

static id _sharedInstance = nil;
+(instancetype)sharedInstance
{
    static dispatch_once_t p;
    dispatch_once(&p, ^{
        _sharedInstance = [[self alloc] init];
    });
    return _sharedInstance;
}