You could create a custom comparer which ignores umlauts:
class IgnoreUmlautComparer : IEqualityComparer<string>
{
    Dictionary<char, char> umlautReplacer = new Dictionary<char, char>()
    {
        {'ä','a'}, {'Ä','A'},
        {'ö','o'}, {'Ö','O'},
        {'ü','u'}, {'Ü','U'},
    };
    Dictionary<string, string> pseudoUmlautReplacer = new Dictionary<string, string>()
    {
        {"ae","a"}, {"Ae","A"},
        {"oe","o"}, {"Oe","O"},
        {"ue","u"}, {"Ue","U"},
    };
    private IEnumerable<char> ignoreUmlaut(string s)
    {
        char value;
        string replaced = new string(s.Select(c => umlautReplacer.TryGetValue(c, out value) ? value : c).ToArray());
        foreach (var kv in pseudoUmlautReplacer)
            replaced = replaced.Replace(kv.Key, kv.Value);
        return replaced;
    }
    public bool Equals(string x, string y)
    {
        var xChars = ignoreUmlaut(x);
        var yChars = ignoreUmlaut(y);
        return xChars.SequenceEqual(yChars);
    }
    public int GetHashCode(string obj)
    {
        return ignoreUmlaut(obj).GetHashCode();
    }
}
Now you can use this comparer with Enumerable methods like Distinct:
string[] allStrings = new[]{"voest","vost","vöst"};
bool allEqual = allStrings.Distinct(new IgnoreUmlautComparer()).Count() == 1;
// --> true