PowerShell Invoke-Expression with ampersand in the command string

The ampersand must be double-quoted inside the string "&", so you need to escape the inner double quotes

$streamout_calmedia01 = "rtmp://...vent`"&`"adbe-record-mode=record"

or put the string in single quotes

$streamout_calmedia01 = 'rtmp://...vent"&"adbe-record-mode=record'