How to invoke webservice from trigger without using @future annotation?

You can use outbound messages which can send a soap request to an endpoint using workflow, or you can use the streaming api where you can create push topics to send push notifications to subscribers.

You can get the help from here about outbound message- https://developer.salesforce.com/docs/atlas.en-us.api.meta/api/sforce_api_om_outboundmessaging_setting_up.htm