To get the query that you are trying to achieve you could try adding a callback to the where method and adding your where/orWhere in there like so:
$query = myTableModel::where(function($query) {
$query->where('id', '>', 78)
->orWhereNotNull('name');
})->where('term_date', '>=', date('Y-m-d'));
Running this on a local User model gives the following when doing a toSql() which is what I believe you're after.
select * from `users` where (`id` > ? or `name` is not null) and `term_date` >= ?