The term "efficiently" can heavily depend on your actual strings and number of them. I've come up with next benchmark (for BenchmarkDotNet) :
public class Replace
{
    private static readonly string S = " ab c\r\n de.\nf";
    private static readonly Regex Reg = new Regex(@"\s+", RegexOptions.Compiled);
    [Benchmark]
    public string SimpleReplace() => S
       .Replace(" ","")
       .Replace("\\r","")
       .Replace("\\n","");
    [Benchmark]
    public string StringBuilder() => new StringBuilder().Append(S)
       .Replace(" ","")
       .Replace("\\r","")
       .Replace("\\n","")
       .ToString();
    [Benchmark]
    public string RegexReplace() => Reg.Replace(S, "");
    [Benchmark]
    public string NewString()
    {
            var arr = new char[S.Length];
            var cnt = 0;
            for (int i = 0; i < S.Length; i++)
            {
                switch(S[i])
                {
                    case ' ':
                    case '\r':
                    case '\n':
                        break;
                    default:
                        arr[cnt] = S[i];
                        cnt++;
                        break;
                }
            }
            return new string(arr, 0, cnt);
    }
    [Benchmark]
    public string NewStringForeach()
    {
        var validCharacters = new char[S.Length];
        var next = 0;
        foreach(var c in S)
        {
            switch(c)
            {
                case ' ':
                case '\r':
                case '\n':
                    // Ignore then
                    break;
                default:
                    validCharacters[next++] = c;
                    break;
            }
        }
        return new string(validCharacters, 0, next);
    }
} 
This gives on my machine:
|          Method |        Mean |     Error |    StdDev |
|---------------- |------------:|----------:|----------:|
|   SimpleReplace |   122.09 ns |  1.273 ns |  1.063 ns |
|   StringBuilder |   311.28 ns |  6.313 ns |  8.850 ns |
|    RegexReplace | 1,194.91 ns | 23.376 ns | 34.265 ns |
|       NewString |    52.26 ns |  1.122 ns |  1.812 ns |
|NewStringForeach |    40.04 ns |  0.877 ns |  1.979 ns |