create wpml-config.xml in wp-content/plugins/newsletter with this content:
<wpml-config>
<admin-texts>
<key name="newsletter">
<key name="profile_text"/>
<key name="profile_email_changed"/>
<key name="profile_error"/>
<key name="confirmation_text"/>
<key name="confirmation_subject"/>
<key name="confirmation_message"/>
<key name="confirmed_text"/>
<key name="confirmed_subject"/>
<key name="confirmed_message"/>
<key name="unsubscription_text"/>
<key name="unsubscription_error_text"/>
<key name="unsubscribed_text"/>
<key name="unsubscribed_subject"/>
<key name="unsubscribed_message"/>
</key>
<key name="newsletter_subscription_template">
<key name="template"/>
</key>
</admin-texts>
</wpml-config>
and you will be able to use wpml string translation to translate messages