To the best of my knowledge, there is no search-engine like portal for Tolkien's published works. There have been many efforts to digitize some of the more popular ones (you can purchase e-books, of course, and the Internet Archive has a few in text-searchable form1), which would allow you to assemble one for yourself (Valorum's suggestion, in a comment on the question), but there are notable gaps in what's available.
The most notable are writings published in issues of Vinyar Tengwar and Parma Eldalamberon, special interest newsletters published by the Elvish Linguistic Fellowship fan group. Both publications have received permission from Christopher Tolkien to publish essays (primarily language-related), but few exist in digitized form. It's this kind of limitation that dooms any attempt to create a "complete" Tolkien search engine: so many of his writings came into existence long before digitization was a thing, and weren't commercial enough to convert.
In theory there's nothing stopping someone from setting up an "incomplete" search engine (aside from the usual legal questions), just focused on the most "narrative" books, but to my knowledge nobody has done it; if they have, it certainly isn't prominent.
While not remotely what you're looking for, an interesting quasi-example is the Eldamo lexicon, which is a reasonably-complete online dictionary of Tolkien's invented languages drawing from most of Tolkien's published word-lists.
1 I'm unclear on the legal implications of this, which is why I'm not posting links