Some HDMI inputs are labelled as HDMI/PC inputs and have less processing active on them. See if your tele has one of these labelled as such and if possible manually change the HDMI input named to “PC” .
Most teles have a GAME mode that can be enabled, but ensure you have all kinds of “Movie Plus” and “100hz” settings off, anything that adds artificial image processing basically.
Futhermore than this, using the specific HDMI-PC channel if there’s one available can go one step further and disable “sharpness” options that sometimes GAME mode settings do not disable. Again knocking input lag down.
Some teles, not all, have very responsive VGA inputs. However for a PS3 with HDCP (copy protection), this might require you to use something like a HDFURY device which would retail around £70 here, this all depends on your setup though. I don’t know if 360 has protection or not.
One final thing, occassionally there are engineer assisted or manual firmware updates to TV that you can get your service centre to arrange or do yourself depending on the model.
Hope it’s a help.