TL;DR
This is the answer:
add_action( 'wp_enqueue_scripts', function() {
wp_dequeue_style( 'evo_font_icons');
wp_deregister_style( 'evo_font_icons');
wp_dequeue_style( 'evcal_cal_default');
wp_deregister_style( 'evcal_cal_default');
wp_dequeue_style( 'evo_single_event');
wp_deregister_style( 'evo_single_event');
wp_dequeue_style( 'evcal_addon_styles');
wp_deregister_style( 'evcal_addon_styles');
wp_dequeue_style( 'evo_addon_styles');
wp_deregister_style( 'evo_addon_styles');
wp_dequeue_style( 'evo_fc_styles');
wp_deregister_style( 'evo_fc_styles');
wp_dequeue_style( 'eventon_dynamic_styles');
wp_deregister_style( 'eventon_dynamic_styles');
wp_dequeue_style( 'evo_TX_styles');
wp_deregister_style( 'evo_TX_styles');
}, 20);
Explanation
First of all: eventON is a pain to override styles with. The default styles are too nested, which makes overriding them inefficient and problematic.
That being said, !important should always work, if not, you are not doing something right within your own stylesheets. You can check if your styles are are even loaded through Google Dev tools, even if they are overriden by eventON.
To answer your question:
You need to use the correct handle to dequeue the styles. In order to get the correct handles, you can use a simple var_dump() of all enqueued styles to see which eventon styles are being used and what their handles are:
<?php
global $wp_styles;
var_dump( $wp_styles );
?>
Based on that, we can modify our dequeue-script as seen above.