$uri = 'https://www.stranger.nl/thisisstrange?date=2015-04-05&value=foo&this#&%*'

$body = @{

    'url' = $uri

}


$body | convertto-json

[Reflection.Assembly]::LoadFile("C:\Program Files\WindowsPowerShell\Modules\newtonsoft.json\1.0.1.2\libs\Newtonsoft.Json.dll") | out-null

[Newtonsoft.Json.JsonConvert]::SerializeObject($body)

When using the Newtonsoft json class the output is being show as expected.

Output:
{
    "url":  "https://www.stranger.nl/thisisstrange?date=2015-04-05\u0026value=fo
o\u0026this#\u0026%*"
}
{"url":"https://www.stranger.nl/thisisstrange?date=2015-04-05&value=foo&this#&%*
"}