It seems to make almost absolutely no difference. I created a test class for this. Over the course of five runs, my output was this:
Run 1:
Arrays.asList() method................: 3231 ms
Arrays.stream() method................: 3111 ms
Stream.of() method....................: 3031 ms
Arrays.asList() (premade array) method: 3086 ms
Arrays.stream() (premade array) method: 3231 ms
Stream.of() (premade array) method....: 3191 ms
Run 2:
Arrays.asList() method................: 3270 ms
Arrays.stream() method................: 3072 ms
Stream.of() method....................: 3086 ms
Arrays.asList() (premade array) method: 3002 ms
Arrays.stream() (premade array) method: 3251 ms
Stream.of() (premade array) method....: 3271 ms
Run 3:
Arrays.asList() method................: 3307 ms
Arrays.stream() method................: 3092 ms
Stream.of() method....................: 2911 ms
Arrays.asList() (premade array) method: 3035 ms
Arrays.stream() (premade array) method: 3241 ms
Stream.of() (premade array) method....: 3241 ms
Run 4:
Arrays.asList() method................: 3630 ms
Arrays.stream() method................: 2981 ms
Stream.of() method....................: 2821 ms
Arrays.asList() (premade array) method: 3058 ms
Arrays.stream() (premade array) method: 3221 ms
Stream.of() (premade array) method....: 3214 ms
Run 5:
Arrays.asList() method................: 3338 ms
Arrays.stream() method................: 3174 ms
Stream.of() method....................: 3262 ms
Arrays.asList() (premade array) method: 3064 ms
Arrays.stream() (premade array) method: 3269 ms
Stream.of() (premade array) method....: 3275 ms
From the output, It looks like the Stream.of() method is very marginally (but consistently) the most efficent, and
Stream.of("hallo","hi").forEach(System.out::println);
is very readable code. Stream.of has the advantage in that it doesn't have to convert the array into a list, or create an array and then create a stream, but can create a stream directly from the elements. What was mildly surprising to me, was that because of the way I did my tests, it was faster to instantiate a new array stream each time with Stream.of() than it was to pass in a pre-made array, probably because "capturing" lambdas - those that reference an external variable - are a little less efficient.
Here's the code for my test class:
import java.util.Arrays;
import java.util.function.Consumer;
import java.util.stream.Stream;
public class StreamArrayTest {
    public static void main(String[] args){
        System.out.println("Arrays.asList() method................: " + arraysAsListMethod() + " ms");
        System.out.println("Arrays.stream() method................: " + arraysStreamMethod() + " ms");
        System.out.println("Stream.of() method....................: " + streamOfMethod() + " ms");
        System.out.println("Arrays.asList() (premade array) method: " + presetArraysAsListMethod() + " ms");
        System.out.println("Arrays.stream() (premade array) method: " + presetArraysStreamMethod() + " ms");
        System.out.println("Stream.of() (premade array) method....: " + presetStreamsOfMethod() + " ms");
    }
    private static Long timeOneMillion(Runnable runner){
        MilliTimer mt = MilliTimer.start();
        for (int i = 0; i < 1000000; i++){
            runner.run();
        }
        return mt.end();
    }
    private static Long timeOneMillion(String[] strings, Consumer<String[]> consumer){
        MilliTimer mt = MilliTimer.start();
        for (int i = 0; i < 1000000; i++){
            consumer.accept(strings);
        }
        return mt.end();        
    }
    public static Long arraysAsListMethod(){
        return timeOneMillion(()->Arrays.asList(new String[]{"hallo","hi","test","test2","test3","test4","test5","test6","test7","test8"}).forEach(StreamArrayTest::doSomething));
    }
    public static Long arraysStreamMethod(){
        return timeOneMillion(()->Arrays.stream(new String[]{"hallo","hi","test","test2","test3","test4","test5","test6","test7","test8"}).forEach(StreamArrayTest::doSomething));
    }
    public static Long streamOfMethod(){
        return timeOneMillion(()->Stream.of("hallo","hi","test","test2","test3","test4","test5","test6","test7","test8").forEach(StreamArrayTest::doSomething));        
    }   
    public static Long presetArraysAsListMethod(){
        String[] strings = new String[]{"hallo","hi","test","test2","test3","test4","test5","test6","test7","test8"};
        return timeOneMillion(strings, (s)->Arrays.asList(s).forEach(StreamArrayTest::doSomething));    
    }
    public static Long presetArraysStreamMethod(){
        String[] strings = new String[]{"hallo","hi","test","test2","test3","test4","test5","test6","test7","test8"};
        return timeOneMillion(strings, (s)->Arrays.stream(s).forEach(StreamArrayTest::doSomething));    
    }
    public static Long presetStreamsOfMethod(){
        String[] strings = new String[]{"hallo","hi","test","test2","test3","test4","test5","test6","test7","test8"};
        return timeOneMillion(strings, (s)->Stream.of(s).forEach(StreamArrayTest::doSomething));    
    }
    public static void doSomething(String s){
        String result = s;
        for (int i = 0; i < 10; i++){
            result = result.concat(s);
        }
    }
}
And the MilliTimer class I used:
public class MilliTimer {
    private long startTime = 0L;
    private MilliTimer(long startTime){
        this.startTime = startTime;
    }
    public static MilliTimer start(){
        return new MilliTimer(System.currentTimeMillis());
    }
    public long end() throws IllegalArgumentException {
        return System.currentTimeMillis() - startTime;
    }
}