It all depends on what you mean by “church”.
In the broadest sense, the church is the community of all baptised Christians, so the assets of the church include the personal assets of all Christians. In the present context that’s obviously much too wide a definition; by no stretch of the imagination are those assets ever going to be available to satisfy judgments obtained by the victims of clerical sexual abuse.
You could narrow it down to the assets of all baptised Catholics, but that’s still much too wide.
More realistically, you could narrow it down to those assets which members of the Church have explicitly set aside to be used specifically for religious purposes. This is a more relevant definition, but in practice it starts to become a very complicated one. Although it is common to present the Catholic church as a centrally organised and controlled monolith, this is not really the case. As previous posters have pointed out, each diocese is an independent entity. So the assets of the diocese of (say) New York are not available to satisfy judgments obtained against the Archbishop of (say) Boston. Moreover, much of the church property which is physically located within a particular diocese will not belong to the diocese. Many schools, and I suspect most hospitals, retreat centres, convents, monasteries, etc do not belong to the diocese at all, but to one of a number of religious orders. The religious orders are not controlled by the dioceses, and their assets are not available to meet judgments against the diocese. (And vice versa; if you were abused by a member of a religious order in a facility operated by that order, your claim is against the order, not the diocese, and your judgment has to be satisfied out of the assets of the order, not the diocese.)
To complicate matters still further, I suspect that in many cases dioceses and/or religious order have no legal existence and/or assets used by a diocese or an order are held, not by the diocese or the order but, as happyheathen suggests, by charitable trusts or foundations whose objects are consistent with the mission of the diocese or order. Depending on how the trust has been structured and on the local law, assets held in this way might not be available to meet judgments against the diocese or the order. I doubt if these structures were established in order to protects assets from the claims of creditors, but in some instances the structures may have that effect.
There will also be assets which have been set aside for explicitly religious purposes but which are not controlled by any diocese or religious order; the assets of the Society of St Vincent de Paul would be an example. These are clearly “church assets” but they are probably not available to meet judgments obtained by those abused by diocesan priests or by members of religious orders (but they probably would be available to meet judgments obtained by people abused by members of the Society acting in the course of the Society’s activities, if there were any such cases).
In short, there isn’t really a single Catholic Church with a vast pool of assets which can be pursued. There is a patchwork of overlapping societies, orders, associations, institutions and charitable foundations, each with its own assets (and many, it has to be said, without very much in the way of assets). Claims are likely to be against one of these, rather than against the Catholic Church as a whole. Suing “the Catholic Church” is a bit like suing “the American people”; you need to be a bit more specific.
But there is one very important qualification to all of this. Earlier threads have discussed the possibility of a claim under the RICO legislation, aimed at organisations like the Mafia but capable of being extended to other areas. I know practically nothing about this, but as I understand it a plaintiff can make the case that individuals or organisations who appear to be legally distinct have in fact been conspiring together to behave unlawfully and, if this is established, then all those involved are liable for the consequences of the unlawful action. And, again, as I understand it, conspiracy can be inferred from a pattern of action which appears to be concerted and common.
I may be completely misrepresenting the position here, and perhaps a US lawyer who actually knows something about the matter will correct me, but this might provide an avenue through which plaintiffs could pursue church assets other than the assets of the diocese or order whose clergy actually perpetrated the abuse.