does the power to interpret the UN charter explicitly fall within the hands of the state parties ? and what would be the consequences of multiple state parties having different interpretations ?
Everyone has the power to interpret the charter, as with any document. The important question is who has the power to resolve disputes of interpretation? Even there, as with most of international law, the answer is more or less "anyone whose authority all parties to the dispute accept."
The charter itself establishes (chapter 14) the International Court of Justice as the UN's "principal judicial organ" (article 92). Members of the United Nations agree to comply with the court's decisions subject to enforcement by the UN Security Council on application of the opposing party (article 94). Article 95, however, says that members may also seek dispute resolution in other tribunals. It does not apply any limits to this freedom, much less exclude disputes of interpretation of the charter itself.
The UN Charter would be interpreted by any entity for which it has relevance, whether judicial, legislative, or executive.
For example, in Canadian law, the United Nations Charter has been relevant for revealing Canada's committment to international human rights norms and the corresponding presumption of conformity that results in domestic law. As that is a matter of domestic law, it is of little significance that states might differ in their precise interpretation of the UN Charter, although given its level of generality and the use to which it would be put in domestic law, the differences would not be significant.
Domestic courts might also look to others' interpretations as a comparative exercise when interpreting; this is another factor that would keep interpretations similar.
Executive and legislative actors would interpret the UN Charter to understand the state's obligations to the world. And they would certainly look to judicial decisions for guidance.
At international law, any UN body can interpret the UN Charter: judicial bodies, committees, special rapporteurs, etc. They of course would look to each others' interpretations, especially that of the ICJ, with the goal of coherence.