Invoke-restmethod or invoke-webrequest?
The Invoke-RestMethod cmdlet uses the default decoding on the result of the HttpWebResponse.CharacterSet property.
If that is not set it uses a default encoding of ISO-8859-1 by default (afaik).
I'm assuming your server is sending some wrong charset in the response headers (or dropping it) hence it's beeing decoded wrongly.
Do you know what charset/encoding are sent in your response from your server?
If you're trying the Invoke-webrequest; check your headers in your response like e.g.
$r = invoke-webrequest http://example.com
$r.Headers
If you're dealing with an encoding issue; e.g. your server is not sending the right headers; you can always try to dump the response in a file and read it with a different encoding:
Invoke-WebRequest http://example.com -outfile .\test.txt
$content = get-content .\test.txt -Encoding utf8 -raw
In this case you will no longer be working with the http-response; but it might help you debug/find the encoding issues your looking for.