Looking at the log there are a lot of entries referring to "PHP Strict Standards". Basically these are coding errors but they are typically suppressed as PHP can interpret what it's supposed to do. So to get rid of those we need to do the updates that are mentioned in your log.
Declaration of WP_SimplePie_Blog_Item::get_id() should be compatible with SimplePie_Item::get_id($hash = false)
Declaration of WP_SimplePie_Blog_Item::get_links() should be compatible with SimplePie_Item::get_links($rel = 'alternate')
I've fixed these two in the dev version.
Declaration of Blogger_Import_List_Table::prepare_items() should be compatible with WP_List_Table::prepare_items()
This one is a bit more challenging, I thing the solution is to pass the data through in the constructor so that prepare_items can be then made parameterless.
There are also a series of calls that are made in the incorrect context i.e. static vs instance. These will each take a bit of investigation
method Blogger_Import::ajax_die() should be declared static or not called statically in blogger-importer.php on line 259
method BloggerEntry::get_post_by_oldID() should be declared static or not called statically in blogger-importer-blog.php on line 218
method CommentEntry::get_comment_by_oldID() should be declared static or not called statically in blogger-importer-blog.php on line 227
method Blogger_Import::_log() should be declared static or not called statically in blogger-importer-blog.php on line 801/802
There is also a mention of:
PHP Notice: The data could not be converted to UTF-8. You MUST have either the iconv or mbstring extension installed. Upgrading to PHP 5.x (which includes iconv) is highly recommended. in /home/u420999827/public_html/wordpress/wp-includes/class-simplepie.php on line 1446
I have had this occur during my imports but have yet to acertain why it occurs. It might be a memory issue. It is NOT the issue mentioned in the message.