How can oceanic sediments become part of continental mountains?

Answer 1

Usually, those are formed when continents collide, like Inda and Asia are doing right now. Before, they were apart, and an ocean separated them. When they crunch, the ocean gets caught up in the collision and forced up.

Answer 2

As an oceanic plate dives underneath a continental plate all the layers of sediment are essentially getting scraped off the surface of the submerging plate and accumulating into whats called an Accretionary Prism. Examples: The Bay Area in California, where San Francisco and Marin County are is all ancient oceanic sediments that were forced upwards up the submerging plate and earthquakes causing uplift.

Answer 3

I'm guessing you are referring to observed sand/limestone and other sedimentary deposits on some mountain ranges. Mountains were not always mountains. In the distant past, some areas that are now mountains were actually under water where they collected sediment.

For example, the mountains surrounding the San Joaquin Valley in California were once flat lands submerged under an inland sea. A number of the mountain ranges around the Mediterranean were similarly flat lands under water until tectonic lifting raised them up.

Hawaii is a prime example of an ongoing process were land under the Pacific Ocean is rising up as mountains...and, of course, they become new islands in the chain of islands we call Hawaii. But meanwhile, while those mountains to be are still under the ocean, they are collecting sediment.