Vegetarian sources of omega-3s provide only ALA (alpha-linolenic acid), a precursor form that the body cannot convert efficiently to the DHA and EPA. Flax oil has ALA which converts to DHA in healthy humans. Since it is from vegetable sources, it may be more available. Walnuts are a good source of the essential fatty acid - ALA, as well. Chai seeds, hemp seeds, mustard oil, beans, and nuts also provide ALA. Wild rice, berries and leafy greens have some ALA.
It is tough getting alternative of fish oil regarding EPA and DHA content. Marine fish is blessed with EPA and DHA (Omega-3 PUFAs) which are scarce in other sources. You may supplement some special plant originated oils as suggested by Dr. Joan Vaccaro.
Algae contains a high ratio of EPA and DHA similar to that found in fish oil. There's products that can be found such as DHAgold which may be used for supplementation and incorporation of omega-3 polyunsaturated fatty acids.