No, the ECHR has no power to order a new trial. What it does have is the authority to tell the signatory state (in this case, the Italian State) to address and remedy the situation. The Italian state would have the obligation to do so, so long as it is a signatory to the European Convention on Human Rights.
How the Italian State chooses to address and remedy the situation would be up to it. For example, if the ECHR were to rule that Knox's human rights were indeed infringed in relation to the criminal slander conviction, the Italian State could choose to remedy this by one of two measures: they could withdraw the prosecution on this charge (meaning that the court would quash the conviction and automatically acquit), or they could choose to retry Knox on this charge, excluding all prosecution evidence which the ECHR has ruled infringed Knox's rights (meaning that essentially it wouldn't be possible to put forward a compelling prosecution case anyhow).
If the Italian State refused or neglected to apply an appropriate remedy, the only other constitutional action available to it would be to withdraw as a signatory to the European Convention on Human Rights - a move that would have widespread ramifications well beyond this case. If the Italian State refused to apply remedies and refused to withdraw as a signatory to the Convention, there would be a constitutional crisis within the European political framework.
So, in summary: while the ECHR cannot tell European Sovereign States to acquit or retry, it can tell these countries to address and remedy the human rights abuses, so long as those countries remain signatories to the Convention. And in practice, this means that the ECHR actually can implicitly force acquittals or retrials - unless and until the country formally withdraws its signature from the Convention.