Not your knives? Why not?
And for the record, I really know very little about Kosher laws.
Kosher 101
1 Certain animals may not be eaten at all. This restriction includes the flesh, organs, eggs and milk of the forbidden animals.
2 Of the animals that may be eaten, the birds and mammals must be killed in accordance with Jewish law.
3 All blood must be drained from meat and poultry or broiled out of it before it is eaten.
4 Certain parts of permitted animals may not be eaten.
5 Fruits and vegetables are permitted, but must be inspected for bugs (which cannot be eaten)
6 Meat (the flesh of birds and mammals) cannot be eaten with dairy. Fish, eggs, fruits, vegetables and grains can be eaten with either meat or dairy. (According to some views, fish may not be eaten with meat).
7 Utensils (including pots and pans and other cooking surfaces) that have come into contact with meat may not be used with dairy, and vice versa. Utensils that have come into contact with non-kosher food may not be used with kosher food. This applies only where the contact occurred while the food was hot.
A utensil picks up the kosher "status" (meat, dairy, pareve, or treif) of the food that is cooked in it or eaten off of it, and transmits that status back to the next food that is cooked in it or eaten off of it. Thus, if you cook chicken soup in a saucepan, the pan becomes meat. If you thereafter use the same saucepan to heat up some warm milk, the fleishik status of the pan is transmitted to the milk, and the milchik status of the milk is transmitted to the pan, making both the pan and the milk a forbidden mixture.
Kosher status can be transmitted from the food to the utensil or from the utensil to the food only in the presence of heat, (including hot spices) or prolonged contact, thus if you are eating cold food in a non-kosher establishment, the condition of the plates is not an issue. You could use the same knife to slice cold cuts and cheese, as long as you clean it in between, but this is not really a recommended procedure, because it increases the likelihood of mistakes.
Stove tops and sinks routinely become non-kosher utensils, because they routinely come in contact with both meat and dairy in the presence of heat. It is necessary, therefore, to use dishpans when cleaning dishes (don't soak them directly in the sink) and to use separate spoon rests and trivets when putting things down on the stove top.
Dishwashers are a kashrut problem. If you are going to use a dishwasher for both meat and dairy in a kosher home, you either need to have separate dish racks or you need to run the dishwasher in between meat and dairy loads.
You should use separate towels and pot holders for meat and dairy. Routine laundering kashers such items, so you can simply launder them between using them for meat and dairy.
8 Grape products made by non-Jews may not be eaten.