以下サンプルでは，単純なテキストファイルを gzip，bzip2 で圧縮されたファイルを読み込むものとします．

gzip はJVM標準のライブラリだけで読み込み可能です．
java.util.zip.GZIPInputStream を利用します．

package hello.compress;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.nio.charset.StandardCharsets;
import java.util.zip.GZIPInputStream;

public class HelloGZipMain {

	public static void main(String[] args) throws Exception {
		File gzFile = new File("hello-compress.txt.gz");
		try (InputStream is = new FileInputStream(gzFile);
				// java.util.zip.GZIPInputStream
				GZIPInputStream gzis = new GZIPInputStream(is);
				InputStreamReader isr = new InputStreamReader(gzis, StandardCharsets.UTF_8);
				BufferedReader br = new BufferedReader(isr);) {
			String s;
			while ((s = br.readLine()) != null) {
				System.err.println(s);
			}
		}
	}
}

bzip2 ファイルは Apache Commons Compress を利用するのがベストかと思います．

package hello.compress;

import java.io.BufferedInputStream;
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;

import org.apache.commons.compress.compressors.CompressorException;
import org.apache.commons.compress.compressors.CompressorInputStream;
import org.apache.commons.compress.compressors.CompressorStreamFactory;

public class HelloBZ2Main {
	public static void main(String[] args) throws Exception {
		File bz2File = new File("hello-compress.txt.bz2");
		// try-with-resources
		try (FileInputStream fis = new FileInputStream(bz2File);
				BufferedInputStream bis = new BufferedInputStream(fis);
				// see https://mvnrepository.com/artifact/org.apache.commons/commons-compress
				// org.apache.commons.compress.compressors.CompressorStreamFactory
				CompressorInputStream cis = new CompressorStreamFactory() //
						.createCompressorInputStream(bis);
				BufferedReader br = new BufferedReader(new InputStreamReader(cis, "UTF-8"));) {
			String line;
			while ((line = br.readLine()) != null) {
				System.err.println(line);
			}
		} catch (CompressorException e) {
			throw new IOException(e);
		}
	}
}

以上．