What is the recommended method of accessing Twitter APIs though Java? I can find few connection libraries:

If you are asking about the Ads API specifically, there’s a Java SDK here based on Twitter4J.

We otherwise would not recommend specific third-party libraries for the broad API, but can talk about which ones we see used most often. For Android, we produce and support our own Twitter Kit. Beyond that, I most commonly see developers using Twitter4J, but that’s not necessarily a personal endorsement as I don’t code Java day-to-day any more!

Thanks @andypiper

Can we access Twitter APIs using curl and not passing the header in the curl.

curl
–get ‘https://api.twitter.com/1.1/search/tweets.json
–data ‘&q=%23archaeology’
–header '‘Authorization: OAuth oauth_consumer_key=“123”, oauth_nonce=“9999”, oauth_signature=“AAAA”, oauth_signature_method=“HMAC-SHA1”, oauth_timestamp=“1450742465”, oauth_token=“9999-AAAA”, oauth_version=“1.0”’
–silent

I have Access Token and Access Token Secret, can I use only these and curl to access the Twitter APIs (no header)?

No, the way OAuth works is that you need to build the authentication data in the HTTP headers. There is no alternative to this.